What is the solution for y^{''}-y=2e^x-1-6*x*e^x ?

The solution for y^{''}-y=2e^x-1-6*x*e^x is y=c_{1}e^x+c_{2}e^{-x}+(-3e^xx^2+5e^xx)/2+1

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y^{''}-y=2e^x-1-6xe^x

y^{^{''}} - y = 2 e^{x} - 1 - 6 \cdot x \cdot e^{x}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{- 3 e ^{x} x ^{2} + 5 e ^{x} x}{2} + 1

Solution steps

y^{''} (x) - y = 2 e^{x} - 1 - 6 \cdot x \cdot e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{- 3 e ^{x} x ^{2} + 5 e ^{x} x}{2} + 1

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{- 3 e ^{x} x ^{2} + 5 e ^{x} x}{2} + 1

What is the solution for y^{''}-y=2e^x-1-6*x*e^x ?
The solution for y^{''}-y=2e^x-1-6*x*e^x is y=c_{1}e^x+c_{2}e^{-x}+(-3e^xx^2+5e^xx)/2+1