What is the solution for y^{''}+3y^'+2y=26x+47 ?

The solution for y^{''}+3y^'+2y=26x+47 is y=c_{1}e^{-x}+c_{2}e^{-2x}+13x+4

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y^{''}+3y^'+2y=26x+47

y^{^{''}} + 3 y^{^{'}} + 2 y = 26 x + 47

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 13 x + 4

Solution steps

y^{''} (x) + 3 y^{'} (x) + 2 y = 26 x + 47

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 13 x + 4

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 13 x + 4

y^{^{''}} + y^{^{'}} = x, y (0) = 8, y^{^{'}} (0) = 0

y^{^{''}} - y^{^{'}} - 6 y = 23 sin (3 x)

y^{^{''}} + 4 y = 3 cos (2 t), y (0) = 1, y^{^{'}} (0) = 0

0.125 y^{^{''}} + 106 y + 1000 = 0

\frac{d ^{2} y}{d x ^{2}} - y = e^{x} sin (x)

What is the solution for y^{''}+3y^'+2y=26x+47 ?
The solution for y^{''}+3y^'+2y=26x+47 is y=c_{1}e^{-x}+c_{2}e^{-2x}+13x+4