Question

Solve differential equation y'+2xy= 4x

First order differential equations
ANSWERED
asked 2021-01-28
Solve differential equation \(y'+2xy= 4x\)

Answers (1)

2021-01-29

\(y'+2xy=4x\)
\(y'=4x-2xy\)
\(dy/dx= x(4-2y)\)
\(dy/(4-2y)= xdx\)
\(\int dy/(4-2y)= \int xdx\)
\((\ln(4-2y))/-2= x^2/2+C\)
\(\ln(4-2y)= -(x^2+2C)\)
\(4-2y= e^{-(x^2+2C)}\)
\(y=(4-e^{-(x^2+2C))}/2\)

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