- #1

ph_xdf

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