Hello all, this is my first post and I'm having trouble with some homework. Here is the problem:(adsbygoogle = window.adsbygoogle || []).push({});

Solve:

[tex]U_x_y - yU_y = e^x[/tex]

I tried subbing [tex]V = U_y[/tex] then I have

[tex]V_x - yV = e^x[/tex]

I solve this as a linear equation with an integrating factor of [tex]e^{-\frac{1}{2}y^2}[/tex]

and get

[tex]V = e^{\frac{1}{2}y^2}*(e^{-\frac{1}{2}y^2} \int e^x dx + f(y))[/tex]

[tex]V = e^x + e^{\frac{1}{2}y^2}*f(y)[/tex]

or

[tex]U_y = e^x + e^{\frac{1}{2}y^2}*f(y)[/tex]

Now, how do I integrate the second part wrt y?

Thanks

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# Homework Help: 2nd order partial differential equation

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