 #1
 2
 2
Homework Statement:
 How do I solve these differential equations?
Relevant Equations:

$$\frac{dy}{dx} = \frac{1}{2 \alpha \beta}  \frac{\cos(x)}{2 \beta \sin(y)} $$
$$\frac{\partial f (x,t)}{\partial t}  \alpha \beta \frac{\partial f (x,t)}{\partial x} \cos(x)+\alpha \beta \sin(x) f (x,t) =0 $$
$$\frac{\partial f (x,t)}{\partial t}  \alpha \beta \frac{\partial f (x,t)}{\partial x} (x \frac{3 \pi}{2})\alpha \beta f (x,t) =0$$
For the first and second, I don't know if there is an analytical solution.
The third I believe can only be solved with: $$ f(x,t)=c e^{\alpha \beta t}$$
The third I believe can only be solved with: $$ f(x,t)=c e^{\alpha \beta t}$$