- #1
mnb96
- 715
- 5
Hello,
do you have any strategy to suggest in order to solve the following system of partial differential equations in x(s,t) and y(s,t)?
[tex]\frac{\partial x}{\partial t} = x - \frac{1}{2}\sin(2x)[/tex]
[tex]\frac{\partial y}{\partial t} = y \; \sin^2(x)[/tex]
(note that the partial differentiation is always with respect to t).
In case it might be useful, I can safely assume that the codomain of x(s,t) and y(s,t) is [-1,1].
I already tried with Maple and Mathematica but they only give me numerical solutions.
An approximation would be ok for me, as long as I get a closed form for x and y.
I was also wondering if you think there might exist another system of coordinates in which this system is easier to solve
Thanks.
do you have any strategy to suggest in order to solve the following system of partial differential equations in x(s,t) and y(s,t)?
[tex]\frac{\partial x}{\partial t} = x - \frac{1}{2}\sin(2x)[/tex]
[tex]\frac{\partial y}{\partial t} = y \; \sin^2(x)[/tex]
(note that the partial differentiation is always with respect to t).
In case it might be useful, I can safely assume that the codomain of x(s,t) and y(s,t) is [-1,1].
I already tried with Maple and Mathematica but they only give me numerical solutions.
An approximation would be ok for me, as long as I get a closed form for x and y.
I was also wondering if you think there might exist another system of coordinates in which this system is easier to solve
Thanks.
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