What is the solution for y^{''}+3y^'=6x+5 ?

The solution for y^{''}+3y^'=6x+5 is y=c_{1}+c_{2}e^{-3x}+x^2+x

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y^{''}+3y^'=6x+5

y^{^{''}} + 3 y^{^{'}} = 6 x + 5

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

Solution steps

y^{''} (x) + 3 y^{'} (x) = 6 x + 5

Solve linear ODE:

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

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

y^{^{''}} + 12 y = 4 e^{9 x}

0.01 y^{^{''}} - 0.06 y^{^{'}} + 0.08 y = 10 x

y^{^{''}} - y^{^{'}} - 2 y = 10, y (- 1) = 0, y^{^{'}} (- 1) = 1

y^{^{''}} - 3 y^{^{'}} + 2 y = 1

y^{^{''}} + 36 y = 288 sin (6 x) + 96 cos (6 x)

What is the solution for y^{''}+3y^'=6x+5 ?
The solution for y^{''}+3y^'=6x+5 is y=c_{1}+c_{2}e^{-3x}+x^2+x