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Question: a problem in change of variables

Question:a problem in change of variables

mehdi jafari 754 Maple 2024
ode differential-equations dchange
August 26 2024
1

Hi dear mapleprime users, i have a problem in a change of varibales if the following ode. i want to use "r=R*rs,u(r)=h*u(R*rs)" variable changes in ode, how can i do that, R is a constant. tnx for the help

> 

restart;with(Student[ODEs]):
> 

y := (1 + diff(u(r), r))*diff(u(r), r, r) + (1 + vs*u(r)/r + (1 - vs)/2*diff(u(r), r))*diff(u(r), r)/r - (1 + (1 + vs)/(2*r)*u(r))*u(r)/r^2

(1+diff(u(r), r))*(diff(diff(u(r), r), r))+(1+vs*u(r)/r+(1/2)*(1-vs)*(diff(u(r), r)))*(diff(u(r), r))/r-(1+(1/2)*(1+vs)*u(r)/r)*u(r)/r^2

 (1)
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constants := constants, R:
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subs(r=R*rs,u(r)=h*u(R*rs),y) ;convert(%,D)

(1+diff(u(R*rs), R*rs))*(diff(diff(u(R*rs), R*rs), R*rs))+(1+vs*u(R*rs)/(R*rs)+(1/2)*(1-vs)*(diff(u(R*rs), R*rs)))*(diff(u(R*rs), R*rs))/(R*rs)-(1+(1/2)*(1+vs)*u(R*rs)/(R*rs))*u(R*rs)/(R^2*rs^2)

  

Error, invalid input: diff received R*rs, which is not valid for its 2nd argument

  
 

 

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