What is the solution for y^{''}-y^'=6xe^x ?

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

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y^{''}-y^'=6xe^x

y^{^{''}} - y^{^{'}} = 6 x e^{x}

y = c_{1} e^{x} + c_{2} + 3 e^{x} x^{2} - 6 (e^{x} x - e^{x})

Solution steps

y^{''} (x) - y^{'} (x) = 6 x e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} + 3 e^{x} x^{2} - 6 (e^{x} x - e^{x})

y = c_{1} e^{x} + c_{2} + 3 e^{x} x^{2} - 6 (e^{x} x - e^{x})

x \to 0 lim (x^{3} - 3 x^{2} + 2 x - 3)

2 y^{^{''}} - 32 y = 0

\frac{d}{d x} (- 12 x^{2})

\int - 4 \cdot sin (2 x) + 3 \cdot cos (3 x) d x

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