What is the solution for (2d^2-d-3)y=25e^{-x} ?

The solution for (2d^2-d-3)y=25e^{-x} is y=c_{1}e^{(3x)/2}+c_{2}e^{-x}-5xe^{-x}

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(2d^2-d-3)y=25e^{-x}

(2 d^{2} - d - 3) y = 25 e^{- x}

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

Solution steps

(2 d^{2} - d - 3) y = 25 e^{- x}

Solve linear ODE:

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

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

(d^{2} - 4 d + 4) \cdot y = 8 x^{2} + e^{2 x}

y^{^{'''}} + 6 y^{^{''}} = x^{2}

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

y^{^{''}} + y^{^{'}} = t^{2} + 2 t

y^{^{''}} + 9 y = 10, e^{- t} y (0) y^{^{'}} (0) = 0

What is the solution for (2d^2-d-3)y=25e^{-x} ?
The solution for (2d^2-d-3)y=25e^{-x} is y=c_{1}e^{(3x)/2}+c_{2}e^{-x}-5xe^{-x}