How do I solve these differential equations?

[ph_xdf]

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

 

[HallsofIvy]

The second and third, as they are written, are not even equations! Was the first "-" in each supposed to be "="?

 

[ph_xdf]

No, the second and the third are equal to zero and I can see it 🤔