- #1
pk415
- 5
- 0
Hello all, this is my first post and I'm having trouble with some homework. Here is the problem:
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
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