
Differential Equations Ordinary and Partial Differential Equations Math Forum 
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March 31st, 2019, 08:43 PM  #1 
Newbie Joined: Mar 2019 From: Russia Posts: 2 Thanks: 0  Partial Differential Equation
Help please, I need to solve this differential equation $\displaystyle x\frac{\partial^2 U}{\partial x^2}+y\frac{\partial^2 U}{\partial y^2}=aU$ in Matlab (where "a" is a constant parameter, it can be taken by any), I wanted to use the Partial Differential Equation Toolbox, but I ran into a problem, the elliptic equation in this Toolbox is represented in a vector form, namely div(c*grad(u))+a*u=f. Please help me convert my equation to this form and tell me how it can be done or at least name the sources of information from which I can learn this knowledge. I really need to solve this equation in Matlab,so please tell me how it can be done. 
April 1st, 2019, 07:20 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics 
You probably can't convert your equation to this form. Your equation is nonlinear and second equation you have written is linear. In the unlikely even that it is possible to convert it then it will be some nonlinear change of coordinates which is nonobvious. Most importantly, there is no canonical or algorithmic way to change your equation to this form.

April 2nd, 2019, 06:20 AM  #3 
Newbie Joined: Mar 2019 From: Russia Posts: 2 Thanks: 0 
Thanks for the answer, in that case could you tell me how to solve it in Matlab? Is there any way to solve this equation using builtin matlab methods, without algorithm processing and writing code from scratch?

April 2nd, 2019, 02:19 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2202 
Your equation is linear; I don't know why SDK thought it isn't.

April 2nd, 2019, 10:59 PM  #5 
Senior Member Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics  

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differential, equation, matlab, partial, pde 
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