What is a particular solution to the differential equation \frac{dy}{dx}=(y+5)(x+2)

Markelovnsl

Markelovnsl

Answered question

2022-04-17

What is a particular solution to the differential equation dydx=(y+5)(x+2) with y(0)=-1?

Answer & Explanation

enchantsyseq

enchantsyseq

Beginner2022-04-18Added 19 answers

Explanation:
separate it first
you get
1y+5dydx=x+2
So integrating
1y+5dydxdx=x+2dx
=1y+5dy=x+2dx
So
=ln(y+5)=x22+2x+C
y(0)=-1
=ln(1+5)=C=ln4
ln(y+5)=x22+2x+ln4
ln(y+54)=x22+2x
y=4ex(x2+2)5

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