What is the solution for y^{''}-3y^'=27x^2 ?

The solution for y^{''}-3y^'=27x^2 is y=c_{1}e^{3x}+c_{2}-3x^3-3x^2-2x

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y^{''}-3y^'=27x^2

y^{^{''}} - 3 y^{^{'}} = 27 x^{2}

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

Solution steps

y^{''} (x) - 3 y^{'} (x) = 27 x^{2}

Solve linear ODE:

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

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

4 y^{^{''}} + 324 y = 8 sin (t)

y^{^{'''}} - y^{^{'}} = 5 cos (2 x) + 7 e^{x} + 2 x^{2}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 36 y = e^{10 x}

y^{^{''}} - 2 y^{^{'}} + 10 y = e x cos (3 x)

5 y^{^{''}} - 2 y^{^{'}} + 80 y = 24 sin (4 t)

What is the solution for y^{''}-3y^'=27x^2 ?
The solution for y^{''}-3y^'=27x^2 is y=c_{1}e^{3x}+c_{2}-3x^3-3x^2-2x