1
$\begingroup$

enter image description here

I'm having a lot of trouble with this question and I can't seem to even figure out where to start. Would anyone be able to help out with this? Thanks :)

$\endgroup$
1
$\begingroup$

$$\frac{\partial G}{\partial t}=A\frac{\partial F}{\partial z}$$ $$\frac{\partial^2 G}{\partial \gamma^2}=\frac{\partial}{\partial \gamma} \left(\frac{\partial F}{\partial x} + \frac{\partial F}{\partial y} \right)%(\gamma+s,\gamma-s,At) =\frac{\partial^2 F}{\partial x^2}+2\frac{\partial^2 F}{\partial y \partial x}+\frac{\partial^2 F}{\partial y^2} $$ $$\frac{\partial^2 G}{\partial s^2}=\frac{\partial}{\partial s} \left(\frac{\partial F}{\partial x} - \frac{\partial F}{\partial y} \right)%(\gamma+s,\gamma-s,At) =\frac{\partial^2 F}{\partial x^2}-2\frac{\partial^2 F}{\partial y \partial x}+\frac{\partial^2 F}{\partial y^2} $$ Thus, $$\frac{\partial^2 G}{\partial s^2}+\frac{\partial^2 G}{\partial \gamma^2}=2\frac{\partial F}{\partial z} $$ and we got that $A=2$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.