What is the solution for y^{''}-y=12x^2+e^x ?

The solution for y^{''}-y=12x^2+e^x is y=c_{1}e^x+c_{2}e^{-x}-12x^2-24+(e^xx)/2

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y^{''}-y=12x^2+e^x

y^{^{''}} - y = 12 x^{2} + e^{x}

y = c_{1} e^{x} + c_{2} e^{- x} - 12 x^{2} - 24 + \frac{e ^{x} x}{2}

Solution steps

y^{''} (x) - y = 12 x^{2} + e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - 12 x^{2} - 24 + \frac{e ^{x} x}{2}

y = c_{1} e^{x} + c_{2} e^{- x} - 12 x^{2} - 24 + \frac{e ^{x} x}{2}

y^{^{''}} - 2 y^{^{'}} + y = sin (x) + 3 cos (2 x)

y^{^{''}} + 4 y = t^{2} + 10 e^{t}

d (x) = \frac{1}{2} x^{2} - 10 x

y^{^{''}} - y = 1.7 sin (t)

y^{^{''}} + y^{^{'}} - 12 y = 2 e^{5 t}

What is the solution for y^{''}-y=12x^2+e^x ?
The solution for y^{''}-y=12x^2+e^x is y=c_{1}e^x+c_{2}e^{-x}-12x^2-24+(e^xx)/2