What is the solution for 6y^{''}-13y^'-5y=5x^3+39x^2-36x-10 ?

The solution for 6y^{''}-13y^'-5y=5x^3+39x^2-36x-10 is y=c_{1}e^{(5x)/2}+c_{2}e^{-x/3}-x^3+2

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6y^{''}-13y^'-5y=5x^3+39x^2-36x-10

6 y^{^{''}} - 13 y^{^{'}} - 5 y = 5 x^{3} + 39 x^{2} - 36 x - 10

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

Solution steps

6 y^{''} (x) - 13 y^{'} (x) - 5 y = 5 x^{3} + 39 x^{2} - 36 x - 10

Solve linear ODE:

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

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

y^{^{''}} - 4 y = 4 t - 4

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 2 y = 6

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - 1 = 0

y^{^{''}} + 9 y = 6 cot (3 t) cos (3 t)

2 y^{^{''}} - 3 y^{^{'}} = 9 x^{2} + 10, y (0) = 1, y^{^{'}} (0) = - 3

What is the solution for 6y^{''}-13y^'-5y=5x^3+39x^2-36x-10 ?
The solution for 6y^{''}-13y^'-5y=5x^3+39x^2-36x-10 is y=c_{1}e^{(5x)/2}+c_{2}e^{-x/3}-x^3+2