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How to integrate this partial differential equation 
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#1
Dec2812, 10:14 AM

P: 40

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. 


#2
Dec2812, 10:24 AM

P: 123

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. 


#3
Dec2812, 07:22 PM

Homework
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P: 9,854




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