- #1
VU2
- 35
- 0
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?
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?