What is the solution for y^{''}-3y^'+2.25y=27(x^2-x) ?

The solution for y^{''}-3y^'+2.25y=27(x^2-x) is y=c_{1}e^{(3x)/2}+c_{2}e^{(3x)/2}x+12x^2+20x+16

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y^{''}-3y^'+2.25y=27(x^2-x)

y^{^{''}} - 3 y^{^{'}} + 2.25 y = 27 (x^{2} - x)

y = c_{1} e^{\frac{3 x}{2}} + c_{2} e^{\frac{3 x}{2}} x + 12 x^{2} + 20 x + 16

Solution steps

y^{''} (x) - 3 y^{'} (x) + 2.25 y = 27 (x^{2} - x)

Solve linear ODE:

y = c_{1} e^{\frac{3 x}{2}} + c_{2} e^{\frac{3 x}{2}} x + 12 x^{2} + 20 x + 16

y = c_{1} e^{\frac{3 x}{2}} + c_{2} e^{\frac{3 x}{2}} x + 12 x^{2} + 20 x + 16

\int (6 x + 2) 3 x^{2} + 2 x d x

\frac{d}{d x} (4 x^{3} - x^{4})

\frac{d y}{d x} = k (10 - y) (5 - y)

\int x^{- 9} d x

\frac{d}{d x} (\frac{( x ^{2} + 2 x - 3 )}{( x + 1 ) ^{2}})

What is the solution for y^{''}-3y^'+2.25y=27(x^2-x) ?
The solution for y^{''}-3y^'+2.25y=27(x^2-x) is y=c_{1}e^{(3x)/2}+c_{2}e^{(3x)/2}x+12x^2+20x+16