# How do I solve these differential equations?

## 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: $$f(x,t)=c e^{\alpha \beta t}$$

Delta2

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