What is a solution to the differential equation \frac{dy}{dx}=20y\cos (-5x)?

daurialebraslmc

daurialebraslmc

Answered question

2022-04-19

What is a solution to the differential equation dydx=20ycos(5x)?

Answer & Explanation

cab65699m

cab65699m

Beginner2022-04-20Added 14 answers

it's separable, so we separate
dydx=20ycos(5x)
1ydydx=20cos(5x)
we integrate
1ydydxdx=20cos(5x)dx
or
1ydy=20cos5xdx as cos(ϕ)=cosϕ
lny=2015sin5x+C
lny=4sin5x+C
lny=4sin5x+C
y=e4sin5x+C=Ce4sin5x

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