# What is the general solution of the differential equation dy/dx=8sin2x?

Milton Anderson 2022-09-12 Answered
What is the general solution of the differential equation $\frac{dy}{dx}=8\mathrm{sin}2x$?
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## Answers (1)

Krista Leon
Answered 2022-09-13 Author has 12 answers
We have:
$\frac{dy}{dx}=8\mathrm{sin}2x$
This is a separable ODE, do we can "separate the variables" to give:

Both integrals are of standard functions, so we can now integrate to get the General Solution:
$y=-\frac{8\mathrm{cos}2x}{2}+C$
$\therefore y=-4\mathrm{cos}2x+C$
$\therefore y=C-4\mathrm{cos}2x$

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