0
$\begingroup$

I know how to solve equations (which does not involve constants) using the DSolve. However, I got an equation that involve constants, i.e. $dy/dt=(\Gamma \cos t+T)y-y^{3}$, where $\Gamma$ and $T$ are constants.

I manually solved it and able to find the solution. However, I want to verify my answer using Mathematica.

How to solve this equation using the DSolve command?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

DSolve usually is able to handle constants. Try

DSolve[y'[t] == (\[CapitalGamma] Cos[t]  + T) y[t] \[Minus] y[t]^3, y, t]
(*{{y -> Function[{t}, -(E^(1/2 (4 t + 2 \[CapitalGamma] Sin[t]))/Sqrt[C[1] - 2 Inactive[Integrate][-E^(2 (2 K[1] + \[CapitalGamma] Sin[K[1]])), {K[1], 1,t}]])]}, 
{y ->Function[{t},E^(1/2 (4 t + 2 \[CapitalGamma] Sin[t]))/Sqrt[C[1] - 2 Inactive[Integrate][-E^(2 (2 K[1] + \[CapitalGamma] Sin[K[1]])), {K[1], 1, t}]]]}}*)
Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.