Question

Solve differential equation y'-y=(3x^2+4x-3)e^x

First order differential equations
ANSWERED
asked 2021-02-02
Solve differential equation \(y'-y=(3x^2+4x-3)e^x\)

Answers (1)

2021-02-03

\(y'-y=(3x^2+4x-3)e^x\)
\(dy/dx+Py=Q\)
P= -1, \(Q=(3x^2+4x-3)e^x\)
\(I.F.= e^{\int -dx}= e^{-x}\)
\(y(I.F.)=\int Q(I.F.)dx+c\)
\(ye^{-x}=\int (3x^2+4x-3)e^x e^{-x} dx+c\)
\(ye^{-x}=\int (3x^2+4x-3)dx+c\)
\(ye^{-x}=\int 3x^2 dx+\int 4xdx-\int 3dx+c\)
\(ye^-x= x^3+2x^2-3x+c\)
\(y= x^3 e^x+2x^2 e^x- 3xe^x+ce^x\)
where c is arbitrary constant

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