Is f(xy)=e^(2y)sin(pix) a Solution to the Differential Equation Given?

[VU2]

let f(xy)=e^(2y)sin(pix), is f a solution to (fxy)^2 -fxx(fyy)=4pi^2 e^(4x)


So I found fxx and fyy and fxy, which are -pi(e^(2y))sin(pix), 4sin(pix)e^(2y), 2pi(e^(2y))cos(pix) respectively,

When i reduced everything i got e^4y(sin^2(pix))+pie^4ycos^2(pix)=pie^(4x). I am assuming it is not a solution to 4pi^2 e^(4x) because first, it doesn't add up, and second, e^(4y) is never e^(4x). Am I right, I am not sure?

 

[haruspex]

You are right that it is not a solution, but I wonder whether it's because there is a typo in the question. Maybe it should say f_xy² -f_xxf_yy=4pi² e^4y

 

[VU2]

Yeah, me too. But the problem on the paper clearly states that. I'll bring it up to my professor. Thanks!