mehdi jafari

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11 years, 301 days

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These are questions asked by mehdi jafari

#first_question :how can i solve set of nonlinear ODEs,faster or using any packages ?
#second_question :what can be some boundary conditions for this type of nonlinear ODEs? how many BCs are required for this set of nonlinear ODEs? ( to use numeric solution)

 


 

restart:with(DEtools):with(DifferentialAlgebra):

eq[1]:=diff(N(r),r$2)+2/r*diff(N(r),r)+diff(phi(r),r)/phi(r)*diff(N(r),r)-mu^2/(32*phi(r))*N(r);

diff(diff(N(r), r), r)+2*(diff(N(r), r))/r+(diff(phi(r), r))*(diff(N(r), r))/phi(r)-(1/32)*mu^2*N(r)/phi(r)

(1)

eq[2]:=diff(phi(r),r$2)+2/r*diff(phi(r),r)-1/2*diff(phi(r),r)^2/phi(r)-8*diff(N(r),r)^2/(omega*(1-2*G*M/r))*phi(r);

diff(diff(phi(r), r), r)+2*(diff(phi(r), r))/r-(1/2)*(diff(phi(r), r))^2/phi(r)-8*(diff(N(r), r))^2*phi(r)/(omega*(1-2*G*M/r))

(2)

dsolve({eq[1],eq[2]});

``


 

Download nonlinear_ODE.mw

i want to solve an ode , but maple return an integral in result, how can i have an answer?


 

restart:

eq:=1/(x*y^(2/3))*8.620689655172415*10^(-16)*(-3.11*10^23*x^2*y^(7/6)-3.92*10^19*y^(25/6)+2.14545039999999*10^29*(0.0108*exp(-45.07/y)+exp(-19.98/y^(1/3)-0.00935317203476387*y^2)))/(x+0.015*y^(1.2));

0.8620689655e-15*(-0.3110000000e24*x^2*y^(7/6)-0.3920000000e20*y^(25/6)+0.2317086432e28*exp(-45.07/y)+0.2145450400e30*exp(-19.98/y^(1/3)-0.935317203476387e-2*y^2))/(x*y^(2/3)*(x+0.15e-1*y^1.2))

(1)

eq:=subs(y=y(t),eq):

 

ans:=dsolve(diff(y(t),t)=eq);

t+Intat((12500/1724137931)*x*_a^(2/3)*(3*_a^(6/5)+200*x)/(49*_a^(25/6)+388750*x^2*_a^(7/6)-2896358040*exp(-(4507/100)/_a)-268181300000*exp(-(1/100000000000000000)*(935317203476387*_a^(7/3)+1998000000000000000)/_a^(1/3))), _a = y(t))+_C1 = 0

(2)

 

 

 


 

Download dsolve.mw

how can i solve this inequality in maple ? i want to solve y in terms of x and then plot y,x
could anyone help? tnx in advance

 


 

restart:

with(SolveTools[Inequality]):

eq:=1/(x*y^(2/3))*8.620689655172415*10^(-16)*(-3.11*10^23*x^2*y^(7/6)-3.92*10^19*y^(25/6)+2.14545039999999*10^29*(0.0108*exp(-45.07/y)+exp(-19.98/y^(1/3)-0.00935317203476387*y^2)))/(x+0.015*y^(1.2));

0.8620689655e-15*(-0.3110000000e24*x^2*y^(7/6)-0.3920000000e20*y^(25/6)+0.2317086432e28*exp(-45.07/y)+0.2145450400e30*exp(-19.98/y^(1/3)-0.935317203476387e-2*y^2))/(x*y^(2/3)*(x+0.15e-1*y^1.2))

(1)

solve({eq>0},y);

Warning, solutions may have been lost

 

 


 

Download solveee.mw

what's the problem with PDE below? tnx for help


 

restart:

PDE:=diff(u(x,t),t)=k*diff(u(x,t),x$2)-h*u(x,t);

diff(u(x, t), t) = k*(diff(diff(u(x, t), x), x))-h*u(x, t)

(1)

IBC := {u(-Pi,t)=u(Pi,t), (D[1](u))(-Pi, t) = (D[1](u))(Pi, t),u(x,0)=sin(x)};

{u(x, 0) = sin(x), u(-Pi, t) = u(Pi, t), (D[1](u))(-Pi, t) = (D[1](u))(Pi, t)}

(2)

pdsolve(PDE,IBC);

Error, (in pdsolve/sys) too many arguments; some or all of the following are wrong: [{u(x, t)}, {u(x, 0) = sin(x), u(-Pi, t) = u(Pi, t), (D[1](u))(-Pi, t) = (D[1](u))(Pi, t)}]

 

 


 

Download PDE_problem.mw

how can i plot tangent function without its Asymptote on kPi/2s ? actuallt i want to plot without its vertical Asymptote, could anybody help? tnx
 

restart:

plot(tan(x),x=-2*Pi..2*Pi,style = line,color = "Blue",legend = "tangent Plot",axes=boxed,gridlines);

 

 


 

Download plot.mw

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