How do I solve these differential equations?

Thread starter ph_xdf
Start date Sep 1, 2019
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Differential Differential equations

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SUMMARY

The discussion centers on solving differential equations, specifically addressing the analytical solutions for three equations presented. The third equation is identified as solvable using the formula $$ f(x,t)=c e^{\alpha \beta t}$$. The participants express confusion regarding the formatting of the equations, particularly questioning whether the first "-" should be an "=" sign. The second and third equations are noted to be equal to zero, indicating a misunderstanding in their representation.

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Understanding of differential equations
Familiarity with analytical solutions
Knowledge of exponential functions
Basic algebraic manipulation skills

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Research methods for solving differential equations analytically
Study the properties of exponential functions in differential equations
Learn about common mistakes in formatting mathematical equations
Explore the implications of equations set equal to zero in differential equations

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Students, mathematicians, and educators involved in solving or teaching differential equations, particularly those seeking clarity on analytical solutions and equation formatting.

Sep 1, 2019

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