What is the solution for y^{''}-4y+3y=2x+1 ?

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

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y^{''}-4y+3y=2x+1

y^{^{''}} - 4 y + 3 y = 2 x + 1

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

Solution steps

y^{''} (x) - 4 y + 3 y = 2 x + 1

Solve linear ODE:

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

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

y^{^{''}} + 4 y = sin (3 t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 6 y^{^{'}} - 7 y = e^{- x}

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- x}

f (x) + f^{^{'}} (x) + f^{^{''}} (x) = x^{5} + 64

y^{^{''''}} + 9 y^{^{''}} = sin (3 t) + t e^{4 t} + 4

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