How to integrate this partial differential equation

  • Thread starter JulieK
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I have the following equation

[itex]\frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0[/itex]

where [itex]y[/itex] is a function of [itex]x[/itex] and [itex]m[/itex] is a function of [itex]y[/itex]. If I integrate this equation first with respect to [itex]y[/itex] should I get a function of [itex]x[/itex] as the constant of integration (say [itex]C\left(x\right)[/itex]) or it is just a constant? If it is a function, how can I then find its form (e.g. polynomial, etc.)? Should I use boundary conditions or I can decide about the form from inspecting the type of the equation.
 
Yes, you should have
[tex]
m(y)\frac{dy}{dx}=C(x)
[/tex]
And therefore you can solve it by
[tex]
m(y)dy=C(x)dx
[/tex]
Which you can integrate.
 

haruspex

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how can I then find its form (e.g. polynomial, etc.)? Should I use boundary conditions or I can decide about the form from inspecting the type of the equation.
You'll have to use boundary conditions. There's nothing in the equation that gives a clue about the form of C(x).
 

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