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How do I solve these differential equations?

  • Thread starter ph_xdf
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  • #1
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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: $$ f(x,t)=c e^{\alpha \beta t}$$
 
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Answers and Replies

  • #2
HallsofIvy
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The second and third, as they are written, are not even equations! Was the first "-" in each supposed to be "="?
 
  • #3
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No, the second and the third are equal to zero and I can see it 🤔
 
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