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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} - 4 y = 2 sin (x) + 4 x^{2}

y^{^{''}} + 2 y^{^{'}} - 3 y = 3 x^{2} - 4 x

y^{^{''}} + 9 y = 18 x + 36 sin (3 x)

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 sin (x)

y^{^{''}} + 2 y^{^{'}} + y = \frac{e ^{x}}{x ^{2}}

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