AHSAN

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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) }$

 

 

 

I am trying to plot the contour plot between eta and x but getting complex value. can anyone help me to resolve it
 

restart

psi := -.5500000000*cosh(eta)/sinh(1.+.5000000000*x^2)-(0.5000000000e-1*(-9.+(10.*(4.412800000*cosh(1.+.5000000000*x^2)*sinh(1.+.5000000000*x^2)-.9000000000*exp(2.*x^2+4.)*exp(-1.*x^2-2.)+1.800000000*exp(x^2+2.)*exp(-1.*x^2-2.)-.9000000000*exp(-1.*x^2-2.)))/(exp(-1.*x^2-2.)*((1.+.5000000000*x^2)*exp(2.*x^2+4.)-2.-.5000000000*x^2+2.*exp(x^2+2.)-1.*exp(2.*x^2+4.)))))*sinh(eta)/cosh(1.+.5000000000*x^2)+(.5000000000*(4.412800000*cosh(1.+.5000000000*x^2)*sinh(1.+.5000000000*x^2)-.9000000000*exp(2.*x^2+4.)*exp(-1.*x^2-2.)+1.800000000*exp(x^2+2.)*exp(-1.*x^2-2.)-.9000000000*exp(-1.*x^2-2.)))*eta/(exp(-1.*x^2-2.)*((1.+.5000000000*x^2)*exp(2.*x^2+4.)-2.-.5000000000*x^2+2.*exp(x^2+2.)-1.*exp(2.*x^2+4.)))+(2.*(-.2750000000*exp(eta)-.2750000000*exp(-1.*eta)))*exp(1.+.5000000000*x^2)/(exp(x^2+2.)-1.)+.2032000000*eta/x^2+0.4000000000e-3*exp(-1.*eta)*(1125.*x^4*exp(2.*eta+1.+.5000000000*x^2)-508.*x^2*exp(2.*eta+1.+.5000000000*x^2)-1125.*x^4*exp(1.+.5000000000*x^2)+4500.*exp(eta)*eta*x^2+508.*x^2*exp(1.+.5000000000*x^2)-2032.*exp(eta)*eta)/(x^2*(x^2*exp(x^2+2.)+x^2+4.))

-.5500000000*cosh(eta)/sinh(1.+.5000000000*x^2)-0.5000000000e-1*(-9.+10.*(4.412800000*cosh(1.+.5000000000*x^2)*sinh(1.+.5000000000*x^2)-.9000000000*exp(2.*x^2+4.)*exp(-1.*x^2-2.)+1.800000000*exp(x^2+2.)*exp(-1.*x^2-2.)-.9000000000*exp(-1.*x^2-2.))/(exp(-1.*x^2-2.)*((1.+.5000000000*x^2)*exp(2.*x^2+4.)-2.-.5000000000*x^2+2.*exp(x^2+2.)-1.*exp(2.*x^2+4.))))*sinh(eta)/cosh(1.+.5000000000*x^2)+.5000000000*(4.412800000*cosh(1.+.5000000000*x^2)*sinh(1.+.5000000000*x^2)-.9000000000*exp(2.*x^2+4.)*exp(-1.*x^2-2.)+1.800000000*exp(x^2+2.)*exp(-1.*x^2-2.)-.9000000000*exp(-1.*x^2-2.))*eta/(exp(-1.*x^2-2.)*((1.+.5000000000*x^2)*exp(2.*x^2+4.)-2.-.5000000000*x^2+2.*exp(x^2+2.)-1.*exp(2.*x^2+4.)))+2.*(-.2750000000*exp(eta)-.2750000000*exp(-1.*eta))*exp(1.+.5000000000*x^2)/(exp(x^2+2.)-1.)+.2032000000*eta/x^2+0.4000000000e-3*exp(-1.*eta)*(1125.*x^4*exp(2.*eta+1.+.5000000000*x^2)-508.*x^2*exp(2.*eta+1.+.5000000000*x^2)-1125.*x^4*exp(1.+.5000000000*x^2)+4500.*exp(eta)*eta*x^2+508.*x^2*exp(1.+.5000000000*x^2)-2032.*exp(eta)*eta)/(x^2*(x^2*exp(x^2+2.)+x^2+4.))

(1)

solve(-.5500000000*cosh(eta)/sinh(1.+.5000000000*x^2)-(0.5000000000e-1*(-9.+(10.*(4.412800000*cosh(1.+.5000000000*x^2)*sinh(1.+.5000000000*x^2)-.9000000000*exp(2.*x^2+4.)*exp(-1.*x^2-2.)+1.800000000*exp(x^2+2.)*exp(-1.*x^2-2.)-.9000000000*exp(-1.*x^2-2.)))/(exp(-1.*x^2-2.)*((1.+.5000000000*x^2)*exp(2.*x^2+4.)-2.-.5000000000*x^2+2.*exp(x^2+2.)-1.*exp(2.*x^2+4.)))))*sinh(eta)/cosh(1.+.5000000000*x^2)+(.5000000000*(4.412800000*cosh(1.+.5000000000*x^2)*sinh(1.+.5000000000*x^2)-.9000000000*exp(2.*x^2+4.)*exp(-1.*x^2-2.)+1.800000000*exp(x^2+2.)*exp(-1.*x^2-2.)-.9000000000*exp(-1.*x^2-2.)))*eta/(exp(-1.*x^2-2.)*((1.+.5000000000*x^2)*exp(2.*x^2+4.)-2.-.5000000000*x^2+2.*exp(x^2+2.)-1.*exp(2.*x^2+4.)))+(2.*(-.2750000000*exp(eta)-.2750000000*exp(-1.*eta)))*exp(1.+.5000000000*x^2)/(exp(x^2+2.)-1.)+.2032000000*eta/x^2+0.4000000000e-3*exp(-1.*eta)*(1125.*x^4*exp(2.*eta+1.+.5000000000*x^2)-508.*x^2*exp(2.*eta+1.+.5000000000*x^2)-1125.*x^4*exp(1.+.5000000000*x^2)+4500.*exp(eta)*eta*x^2+508.*x^2*exp(1.+.5000000000*x^2)-2032.*exp(eta)*eta)/(x^2*(x^2*exp(x^2+2.)+x^2+4.)) = 0, eta)

(1250.*x^2*(exp(1.+.5000000000*x^2))^8+125.*x^2*(exp(1.+.5000000000*x^2))^6-254.*(exp(1.+.5000000000*x^2))^8+125.*x^2*exp(x^2+2.+2.*RootOf(-1250*x^2*(exp(1+(1/2)*x^2))^8-381*x^2*exp(3*x^2+_Z+6)+254*_Z*exp(3*x^2+_Z+6)-125*x^2*(exp(1+(1/2)*x^2))^6+254*(exp(1+(1/2)*x^2))^8-3375*x^2*exp(2*x^2+_Z+4)-762*exp(3*x^2+_Z+6)-125*x^2*exp(x^2+2*_Z+2)+2250*_Z*exp(2*x^2+_Z+4)-3004*(exp(1+(1/2)*x^2))^6+3756*x^2*exp(x^2+_Z+2)-6750*exp(2*x^2+_Z+4)-1250*x^2*(exp(_Z))^2-254*exp(x^2+2*_Z+2)-2504*_Z*exp(x^2+_Z+2)+7512*exp(x^2+_Z+2)-2496*(exp(_Z))^2))+3004.*(exp(1.+.5000000000*x^2))^6+1250.*x^2*(exp(RootOf(-1250*x^2*(exp(1+(1/2)*x^2))^8-381*x^2*exp(3*x^2+_Z+6)+254*_Z*exp(3*x^2+_Z+6)-125*x^2*(exp(1+(1/2)*x^2))^6+254*(exp(1+(1/2)*x^2))^8-3375*x^2*exp(2*x^2+_Z+4)-762*exp(3*x^2+_Z+6)-125*x^2*exp(x^2+2*_Z+2)+2250*_Z*exp(2*x^2+_Z+4)-3004*(exp(1+(1/2)*x^2))^6+3756*x^2*exp(x^2+_Z+2)-6750*exp(2*x^2+_Z+4)-1250*x^2*(exp(_Z))^2-254*exp(x^2+2*_Z+2)-2504*_Z*exp(x^2+_Z+2)+7512*exp(x^2+_Z+2)-2496*(exp(_Z))^2)))^2+254.*exp(x^2+2.+2.*RootOf(-1250*x^2*(exp(1+(1/2)*x^2))^8-381*x^2*exp(3*x^2+_Z+6)+254*_Z*exp(3*x^2+_Z+6)-125*x^2*(exp(1+(1/2)*x^2))^6+254*(exp(1+(1/2)*x^2))^8-3375*x^2*exp(2*x^2+_Z+4)-762*exp(3*x^2+_Z+6)-125*x^2*exp(x^2+2*_Z+2)+2250*_Z*exp(2*x^2+_Z+4)-3004*(exp(1+(1/2)*x^2))^6+3756*x^2*exp(x^2+_Z+2)-6750*exp(2*x^2+_Z+4)-1250*x^2*(exp(_Z))^2-254*exp(x^2+2*_Z+2)-2504*_Z*exp(x^2+_Z+2)+7512*exp(x^2+_Z+2)-2496*(exp(_Z))^2))+2496.*(exp(RootOf(-1250*x^2*(exp(1+(1/2)*x^2))^8-381*x^2*exp(3*x^2+_Z+6)+254*_Z*exp(3*x^2+_Z+6)-125*x^2*(exp(1+(1/2)*x^2))^6+254*(exp(1+(1/2)*x^2))^8-3375*x^2*exp(2*x^2+_Z+4)-762*exp(3*x^2+_Z+6)-125*x^2*exp(x^2+2*_Z+2)+2250*_Z*exp(2*x^2+_Z+4)-3004*(exp(1+(1/2)*x^2))^6+3756*x^2*exp(x^2+_Z+2)-6750*exp(2*x^2+_Z+4)-1250*x^2*(exp(_Z))^2-254*exp(x^2+2*_Z+2)-2504*_Z*exp(x^2+_Z+2)+7512*exp(x^2+_Z+2)-2496*(exp(_Z))^2)))^2)/((254.*(exp(1.+.5000000000*x^2))^6+2250.*(exp(1.+.5000000000*x^2))^4-2504.*(exp(1.+.5000000000*x^2))^2)*exp(RootOf(-1250*x^2*(exp(1+(1/2)*x^2))^8-381*x^2*exp(3*x^2+_Z+6)+254*_Z*exp(3*x^2+_Z+6)-125*x^2*(exp(1+(1/2)*x^2))^6+254*(exp(1+(1/2)*x^2))^8-3375*x^2*exp(2*x^2+_Z+4)-762*exp(3*x^2+_Z+6)-125*x^2*exp(x^2+2*_Z+2)+2250*_Z*exp(2*x^2+_Z+4)-3004*(exp(1+(1/2)*x^2))^6+3756*x^2*exp(x^2+_Z+2)-6750*exp(2*x^2+_Z+4)-1250*x^2*(exp(_Z))^2-254*exp(x^2+2*_Z+2)-2504*_Z*exp(x^2+_Z+2)+7512*exp(x^2+_Z+2)-2496*(exp(_Z))^2)))

(2)

with(plots)

contourplot(eta, x = -1 .. 1)

Error, (in plots:-contourplot) invalid input: `plots/contplot` uses a 3rd argument, r2 (of type {range, name = range}), which is missing

 

``


 

Download Help_on_countour_plot.mw

Hi, I want to solve first order ode by using a numerical technique called shooting method, can anyone help me to write an algorithm for the
 

restart

sigma := x^2+1

x^2+1

(1)

M := .1

.1

(2)

N := .5

.5

(3)

``

diff(P(x), x) = -(3*(M-1))/(2*sigma^2)-3*N/sigma^3

diff(P(x), x) = 1.350000000/(x^2+1)^2-1.5/(x^2+1)^3

(4)

``

NULL

ics := P(-infinity) = 0

P(-infinity) = 0

(5)

``


 

Download Shooting_Help.mw
 

restart

sigma := x^2+1

x^2+1

(1)

M := .1

.1

(2)

N := .5

.5

(3)

``

diff(P(x), x) = -(3*(M-1))/(2*sigma^2)-3*N/sigma^3

diff(P(x), x) = 1.350000000/(x^2+1)^2-1.5/(x^2+1)^3

(4)

``

NULL

ics := P(-infinity) = 0

P(-infinity) = 0

(5)

``


 

Download Shooting_Help.mw

 

shooting method. please find attachment

Hello admins. Can you please guide me on what's going wrong with my post? I just posted and now my post has been deleted or vanished?

Hello experts,I need your help to obtain the solution of the mentioned equation in the attached picture by using the newton method by supposing the random value of involved constant like D  etc. I need an algorithm for the newton method for the mentioned equation. note h=1+x^2/2

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