What is a particular solution to the differential equation \frac{dy}{dx}=2xy

Ekwadorkadba3

Ekwadorkadba3

Answered question

2022-04-16

What is a particular solution to the differential equation dydx=2xy with y(0)=3?

Answer & Explanation

davelucasnp0j

davelucasnp0j

Beginner2022-04-17Added 16 answers

y'=2xy
separate it out
1yt=2x
integrate
1yydx=2xdx
1ydy=2xdx
lny=x2+C   
y=ex2+C=Cex2 [C's just any constant]
3=Ce02C=3
So
y=3ex2
strictly speaking, should be ln|y|=x2+C with |y|=Cex2

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