AHSAN

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0 years, 260 days

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These are questions asked by AHSAN

I have an implicit relation in lambda and x, so I am unable to find the value of x in terms of lambda so I generate a set of data points for different values of  x=0,0.1...0.9 and obtained the value of lambda. so my question is how to write a polynomial in terms of lambda for generated data by using curve fitting and how do I checked that the obtained polynomial is correct? pls have look at my maple sheet
 

restart

``

lambda1 := -(3*(-6.003*(1+(1/2)*x^2)^3+15.400672*(1+(1/2)*x^2)^2-8.745236204-7.393580208*x^2))/(20*(1+(1/2)*x^2)^4)

-(3/20)*(-6.003*(1+(1/2)*x^2)^3+15.400672*(1+(1/2)*x^2)^2-8.745236204-7.393580208*x^2)/(1+(1/2)*x^2)^4

(1)

lambda := x -> -1/20*(3*(-1)*6.003*(1 + 1/2*x^2)^3 + 3*15.400672*(1 + 1/2*x^2)^2 + 3*(-8.745236204) + 3*(-1)*7.393580208*x^2)/(1 + 1/2*x^2)^4

proc (x) options operator, arrow; -(1/20)*((-3)*6.003*((1+(1/2)*x^2)^3)+3*15.400672*((1+(1/2)*x^2)^2)+(-3)*8.745236204+(-3)*7.393580208*(x^2))/(1+(1/2)*x^2)^4 end proc

(2)

``

data := [[-0.9786536940e-1, 0], [-0.9445602756e-1, .1], [-0.8473253146e-1, .2], [-0.7004169606e-1, .3], [-0.5215959008e-1, .4], [-0.3283205398e-1, .5], [-0.1345044656e-1, .6], [0.5065808031e-2, .7], [0.2221891323e-1, .8], [0.3780341349e-1, .9], [0.5177568628e-1, 1.0]]

[[-0.9786536940e-1, 0], [-0.9445602756e-1, .1], [-0.8473253146e-1, .2], [-0.7004169606e-1, .3], [-0.5215959008e-1, .4], [-0.3283205398e-1, .5], [-0.1345044656e-1, .6], [0.5065808031e-2, .7], [0.2221891323e-1, .8], [0.3780341349e-1, .9], [0.5177568628e-1, 1.0]]

(3)

``


 

Download Help_polynomial.mw

Hi everyone, I am trying to dsolve a ode but could not get the answer, could anyone please help me or guide me what's wrong with my worksheet


 

restart

u := -3*beta*(2*p^3*sigma^4*(1/3)+(2*p^3*y^2*(1/3)-4*q*(1/3))*sigma^2-4*p^2*y*(k+1)*sigma*(1/3)+p*(k+1)^2)*(y+sigma)*(y-sigma)/(8*sigma^2)+(-p*sigma^3+(p*y^2-k+1)*sigma-(k+1)*y)/(2*sigma)

-(3/8)*beta*((2/3)*p^3*sigma^4+((2/3)*p^3*y^2-(4/3)*q)*sigma^2-(4/3)*p^2*y*(k+1)*sigma+p*(k+1)^2)*(y+sigma)*(y-sigma)/sigma^2+(1/2)*(-p*sigma^3+(p*y^2-k+1)*sigma-(k+1)*y)/sigma

(1)

ode := diff(theta(y), y, y)+G*(diff(u(y), y))^2+G*beta*(diff(u(y), y))^4

diff(diff(theta(y), y), y)+G*(-(3/8)*(diff(beta(y), y))*((2/3)*p(y)^3*sigma(y)^4+((2/3)*p(y)^3*y(y)^2-(4/3)*q(y))*sigma(y)^2-(4/3)*p(y)^2*y(y)*(k(y)+1)*sigma(y)+p(y)*(k(y)+1)^2)*(y(y)+sigma(y))*(y(y)-sigma(y))/sigma(y)^2-(3/8)*beta(y)*(2*p(y)^2*sigma(y)^4*(diff(p(y), y))+(8/3)*p(y)^3*sigma(y)^3*(diff(sigma(y), y))+(2*p(y)^2*y(y)^2*(diff(p(y), y))+(4/3)*p(y)^3*y(y)*(diff(y(y), y))-(4/3)*(diff(q(y), y)))*sigma(y)^2+2*((2/3)*p(y)^3*y(y)^2-(4/3)*q(y))*sigma(y)*(diff(sigma(y), y))-(8/3)*p(y)*y(y)*(k(y)+1)*sigma(y)*(diff(p(y), y))-(4/3)*p(y)^2*(diff(y(y), y))*(k(y)+1)*sigma(y)-(4/3)*p(y)^2*y(y)*(diff(k(y), y))*sigma(y)-(4/3)*p(y)^2*y(y)*(k(y)+1)*(diff(sigma(y), y))+(diff(p(y), y))*(k(y)+1)^2+2*p(y)*(k(y)+1)*(diff(k(y), y)))*(y(y)+sigma(y))*(y(y)-sigma(y))/sigma(y)^2-(3/8)*beta(y)*((2/3)*p(y)^3*sigma(y)^4+((2/3)*p(y)^3*y(y)^2-(4/3)*q(y))*sigma(y)^2-(4/3)*p(y)^2*y(y)*(k(y)+1)*sigma(y)+p(y)*(k(y)+1)^2)*(diff(y(y), y)+diff(sigma(y), y))*(y(y)-sigma(y))/sigma(y)^2-(3/8)*beta(y)*((2/3)*p(y)^3*sigma(y)^4+((2/3)*p(y)^3*y(y)^2-(4/3)*q(y))*sigma(y)^2-(4/3)*p(y)^2*y(y)*(k(y)+1)*sigma(y)+p(y)*(k(y)+1)^2)*(y(y)+sigma(y))*(diff(y(y), y)-(diff(sigma(y), y)))/sigma(y)^2+(3/4)*beta(y)*((2/3)*p(y)^3*sigma(y)^4+((2/3)*p(y)^3*y(y)^2-(4/3)*q(y))*sigma(y)^2-(4/3)*p(y)^2*y(y)*(k(y)+1)*sigma(y)+p(y)*(k(y)+1)^2)*(y(y)+sigma(y))*(y(y)-sigma(y))*(diff(sigma(y), y))/sigma(y)^3+(1/2)*(-(diff(p(y), y))*sigma(y)^3-3*p(y)*sigma(y)^2*(diff(sigma(y), y))+((diff(p(y), y))*y(y)^2+2*p(y)*y(y)*(diff(y(y), y))-(diff(k(y), y)))*sigma(y)+(p(y)*y(y)^2-k(y)+1)*(diff(sigma(y), y))-(diff(k(y), y))*y(y)-(k(y)+1)*(diff(y(y), y)))/sigma(y)-(1/2)*(-p(y)*sigma(y)^3+(p(y)*y(y)^2-k(y)+1)*sigma(y)-(k(y)+1)*y(y))*(diff(sigma(y), y))/sigma(y)^2)^2+G*beta*(-(3/8)*(diff(beta(y), y))*((2/3)*p(y)^3*sigma(y)^4+((2/3)*p(y)^3*y(y)^2-(4/3)*q(y))*sigma(y)^2-(4/3)*p(y)^2*y(y)*(k(y)+1)*sigma(y)+p(y)*(k(y)+1)^2)*(y(y)+sigma(y))*(y(y)-sigma(y))/sigma(y)^2-(3/8)*beta(y)*(2*p(y)^2*sigma(y)^4*(diff(p(y), y))+(8/3)*p(y)^3*sigma(y)^3*(diff(sigma(y), y))+(2*p(y)^2*y(y)^2*(diff(p(y), y))+(4/3)*p(y)^3*y(y)*(diff(y(y), y))-(4/3)*(diff(q(y), y)))*sigma(y)^2+2*((2/3)*p(y)^3*y(y)^2-(4/3)*q(y))*sigma(y)*(diff(sigma(y), y))-(8/3)*p(y)*y(y)*(k(y)+1)*sigma(y)*(diff(p(y), y))-(4/3)*p(y)^2*(diff(y(y), y))*(k(y)+1)*sigma(y)-(4/3)*p(y)^2*y(y)*(diff(k(y), y))*sigma(y)-(4/3)*p(y)^2*y(y)*(k(y)+1)*(diff(sigma(y), y))+(diff(p(y), y))*(k(y)+1)^2+2*p(y)*(k(y)+1)*(diff(k(y), y)))*(y(y)+sigma(y))*(y(y)-sigma(y))/sigma(y)^2-(3/8)*beta(y)*((2/3)*p(y)^3*sigma(y)^4+((2/3)*p(y)^3*y(y)^2-(4/3)*q(y))*sigma(y)^2-(4/3)*p(y)^2*y(y)*(k(y)+1)*sigma(y)+p(y)*(k(y)+1)^2)*(diff(y(y), y)+diff(sigma(y), y))*(y(y)-sigma(y))/sigma(y)^2-(3/8)*beta(y)*((2/3)*p(y)^3*sigma(y)^4+((2/3)*p(y)^3*y(y)^2-(4/3)*q(y))*sigma(y)^2-(4/3)*p(y)^2*y(y)*(k(y)+1)*sigma(y)+p(y)*(k(y)+1)^2)*(y(y)+sigma(y))*(diff(y(y), y)-(diff(sigma(y), y)))/sigma(y)^2+(3/4)*beta(y)*((2/3)*p(y)^3*sigma(y)^4+((2/3)*p(y)^3*y(y)^2-(4/3)*q(y))*sigma(y)^2-(4/3)*p(y)^2*y(y)*(k(y)+1)*sigma(y)+p(y)*(k(y)+1)^2)*(y(y)+sigma(y))*(y(y)-sigma(y))*(diff(sigma(y), y))/sigma(y)^3+(1/2)*(-(diff(p(y), y))*sigma(y)^3-3*p(y)*sigma(y)^2*(diff(sigma(y), y))+((diff(p(y), y))*y(y)^2+2*p(y)*y(y)*(diff(y(y), y))-(diff(k(y), y)))*sigma(y)+(p(y)*y(y)^2-k(y)+1)*(diff(sigma(y), y))-(diff(k(y), y))*y(y)-(k(y)+1)*(diff(y(y), y)))/sigma(y)-(1/2)*(-p(y)*sigma(y)^3+(p(y)*y(y)^2-k(y)+1)*sigma(y)-(k(y)+1)*y(y))*(diff(sigma(y), y))/sigma(y)^2)^4

(2)

dsolve(ode)

Error, (in dsolve) Required a specification of the indeterminate function

 

bc := theta(-sigma) = 0, theta(sigma) = 1

theta(-sigma) = 0, theta(sigma) = 1

(3)

sol := dsolve({bc, ode})

(4)

``


 

Download help_ode.mw

Hi, i am using solve and solve command to find the root but when i used fsolve command to separate only real root, could separate all roots, can anyone correct me, please


 

restart

f := 9.765625000*10^(-6)*(-6671.221362*(x^2+2)^5*sqrt(2)*arctan((1/2)*x*sqrt(2))*x-555.9351135*(x^2+2)^6/((1/2)*x^2+1)-10479.13001*(x^2+2)^5*sqrt(2)*x-(374220*(0.297116730e-1*x^9+.269385824*x^7+.99643086*x^5+5.18951288*x^3+4.42867382*x))*x-1111.870227*x^10-12601.19538*x^8-62147.39274*x^6-485504.8775*x^4-828649.1585*x^2-788850.2769)/(x^2+2)^6-(0.1171875000e-3*(-555.9351135*(x^2+2)^6*sqrt(2)*arctan((1/2)*x*sqrt(2))-873.2608343*(x^2+2)^6*sqrt(2)-(374220*(0.29711673e-2*x^10+0.33673228e-1*x^8+.16607181*x^6+1.29737822*x^4+2.21433691*x^2+2.107985348))*x))*x/(x^2+2)^7+(3.484800000*sqrt(2)*(x^2+2)*arctan((1/2)*x*sqrt(2))*x+.8712000000*(x^2+2)^2/((1/2)*x^2+1)+(5.473911040*(x^2+2))*sqrt(2)*x+5.227200000*x^2-22.99200001)/(16*(x^2+2)^2)-(.8712000000*sqrt(2)*(x^2+2)^2*arctan((1/2)*x*sqrt(2))+1.368477760*sqrt(2)*(x^2+2)^2-36*x*(-0.484000000e-1*x^2+.638666667))*x/(4*(x^2+2)^3)

0.9765625000e-5*(-6671.221362*(x^2+2)^5*2^(1/2)*arctan((1/2)*x*2^(1/2))*x-555.9351135*(x^2+2)^6/((1/2)*x^2+1)-10479.13001*(x^2+2)^5*2^(1/2)*x-374220*(0.297116730e-1*x^9+.269385824*x^7+.99643086*x^5+5.18951288*x^3+4.42867382*x)*x-1111.870227*x^10-12601.19538*x^8-62147.39274*x^6-485504.8775*x^4-828649.1585*x^2-788850.2769)/(x^2+2)^6-0.1171875000e-3*(-555.9351135*(x^2+2)^6*2^(1/2)*arctan((1/2)*x*2^(1/2))-873.2608343*(x^2+2)^6*2^(1/2)-374220*(0.29711673e-2*x^10+0.33673228e-1*x^8+.16607181*x^6+1.29737822*x^4+2.21433691*x^2+2.107985348)*x)*x/(x^2+2)^7+(1/16)*(3.484800000*2^(1/2)*(x^2+2)*arctan((1/2)*x*2^(1/2))*x+.8712000000*(x^2+2)^2/((1/2)*x^2+1)+5.473911040*(x^2+2)*2^(1/2)*x+5.227200000*x^2-22.99200001)/(x^2+2)^2-(1/4)*(.8712000000*2^(1/2)*(x^2+2)^2*arctan((1/2)*x*2^(1/2))+1.368477760*2^(1/2)*(x^2+2)^2-36*x*(-0.484000000e-1*x^2+.638666667))*x/(x^2+2)^3

(1)

ip := solve(f = 0, x)

.6540411301, 3126.002498+5414.398621*I, .4137989369+1.038962897*I, .6364817315+1.870977651*I, -.6364817315+1.870977651*I, -.4137989369+1.038962897*I, -.6540411301, -6252.010299, -.4137989369-1.038962897*I, -.6364817315-1.870977651*I, .6364817315-1.870977651*I, .4137989369-1.038962897*I, 3126.002498-5414.398621*I

(2)

cp := fsolve(numer(f) = 0, x)

.6540411302

(3)

``


 

Download help_fsolve_real_root.mw

Dear community, please help me to verify that the obtained solution by using the fsolve command of maple is correct or wrong? and one more question how to generate interval in which our solution should be contained. dear admin if my question is duplicate please do not delete. please have a look on my maple file

Help.mw

Hi, I generated latex formate of an equation by using a command of maple but when I paste it into MathType, could not get the required equation, can anyone help me

${\frac {1}{51200\, \left( {x}^{2}+2 \right) ^{6}} \left( -187110\,

 \left( {x}^{2}+2 \right) ^{6}\sqrt {2} \left( {Q}^{3}+ \left( {\frac

{18\,k}{11}}-{\frac{18}{11}} \right) {Q}^{2}+ \left( {\frac {320\,{k}^

{2}}{297}}-{\frac {40\,k}{27}}+{\frac{320}{297}} \right) Q+{\frac {80

\,{k}^{3}}{297}}-{\frac {80\,{k}^{2}}{189}}+{\frac {80\,k}{189}}+{

\frac {640\,\lambda}{2079}}-{\frac{80}{297}} \right) \arctan \left( 1/

2\,x\sqrt {2} \right) -93555\, \left( {x}^{2}+2 \right) ^{6}\pi\,

 \left( {Q}^{3}+ \left( {\frac {18\,k}{11}}-{\frac{18}{11}} \right) {Q

}^{2}+ \left( {\frac {320\,{k}^{2}}{297}}-{\frac {40\,k}{27}}+{\frac{

320}{297}} \right) Q+{\frac {80\,{k}^{3}}{297}}-{\frac {80\,{k}^{2}}{

189}}+{\frac {80\,k}{189}}+{\frac {640\,\lambda}{2079}}-{\frac{80}{297

}} \right) \sqrt {2}-374220\, \left(  \left( {Q}^{3}+ \left( {\frac {

18\,k}{11}}-{\frac{18}{11}} \right) {Q}^{2}+ \left( {\frac {320\,{k}^{

2}}{297}}-{\frac {40\,k}{27}}+{\frac{320}{297}} \right) Q+{\frac {80\,

{k}^{3}}{297}}-{\frac {80\,{k}^{2}}{189}}+{\frac {80\,k}{189}}+{\frac

{640\,\lambda}{2079}}-{\frac{80}{297}} \right) {x}^{10}+ \left( {

\frac {34\,{Q}^{3}}{3}}+ \left( {\frac {204\,k}{11}}-{\frac{204}{11}}

 \right) {Q}^{2}+ \left( {\frac {10880\,{k}^{2}}{891}}-{\frac {1360\,k

}{81}}+{\frac{10880}{891}} \right) Q+{\frac {2720\,{k}^{3}}{891}}-{

\frac {2720\,{k}^{2}}{567}}+{\frac {2720\,k}{567}}+{\frac {21760\,

\lambda}{6237}}-{\frac{2720}{891}} \right) {x}^{8}+ \left( {\frac {264

\,{Q}^{3}}{5}}+ \left( {\frac {432\,k}{5}}-{\frac{432}{5}} \right) {Q}

^{2}+ \left( {\frac {512\,{k}^{2}}{9}}-{\frac {704\,k}{9}}+{\frac{512}

{9}} \right) Q+{\frac {128\,{k}^{3}}{9}}-{\frac {1408\,{k}^{2}}{63}}+{

\frac {1408\,k}{63}}+{\frac {97280\,\lambda}{6237}}-{\frac{128}{9}}

 \right) {x}^{6}+ \left( {\frac {4496\,{Q}^{3}}{35}}+ \left( {\frac {

80928\,k}{385}}-{\frac{80928}{385}} \right) {Q}^{2}+ \left( {\frac {

287744\,{k}^{2}}{2079}}-{\frac {35968\,k}{189}}+{\frac{287744}{2079}}

 \right) Q+{\frac {3328\,{k}^{3}}{99}}-{\frac {3328\,{k}^{2}}{63}}+{

\frac {3328\,k}{63}}+{\frac {10240\,\lambda}{297}}-{\frac{3328}{99}}

 \right) {x}^{4}+ \left( {\frac {10672\,{Q}^{3}}{63}}+ \left( {\frac {

21344\,k}{77}}-{\frac{21344}{77}} \right) {Q}^{2}+ \left( {\frac {

1094656\,{k}^{2}}{6237}}-{\frac {136832\,k}{567}}+{\frac{1094656}{6237

}} \right) Q+{\frac {35584\,{k}^{3}}{891}}-{\frac {35584\,{k}^{2}}{567

}}+{\frac {35584\,k}{567}}+{\frac {235520\,\lambda}{6237}}-{\frac{

35584}{891}} \right) {x}^{2}+{\frac {25376\,{Q}^{3}}{231}}+ \left( {

\frac {12352\,k}{77}}-{\frac{12352}{77}} \right) {Q}^{2}+ \left( -{

\frac {7936\,k}{63}}+{\frac {63488\,{k}^{2}}{693}}+{\frac{63488}{693}}

 \right) Q-{\frac{512}{27}}+{\frac {512\,{k}^{3}}{27}}-{\frac {5632\,{

k}^{2}}{189}}+{\frac {102400\,\lambda}{6237}}+{\frac {5632\,k}{189}}

 \right) x \right) }$

 

 

 

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