What is the solution for (D^2+3D-10)y=20+5e^{3x} ?

The solution for (D^2+3D-10)y=20+5e^{3x} is y=c_{1}e^{2x}+c_{2}e^{-5x}-2+5/8 e^{3x}

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(D^2+3D-10)y=20+5e^{3x}

(D^{2} + 3 D - 10) y = 20 + 5 e^{3 x}

y = c_{1} e^{2 x} + c_{2} e^{- 5 x} - 2 + \frac{5}{8} e^{3 x}

Solution steps

(D^{2} + 3 D - 10) y = 20 + 5 e^{3 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 5 x} - 2 + \frac{5}{8} e^{3 x}

y = c_{1} e^{2 x} + c_{2} e^{- 5 x} - 2 + \frac{5}{8} e^{3 x}

(D^{4} + 4 D^{2}) y = sin (2 x) + x e^{x} + 4

y^{^{''}} + 5 \frac{d y}{d x} - 6 y = 2 + (- 2) sin (2 x)

y^{^{''}} - y^{^{'}} + 6 y = 3 sin (2 x) + 4 cos (2 x)

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{- 3 t}, y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} + x = 4 e^{t}

What is the solution for (D^2+3D-10)y=20+5e^{3x} ?
The solution for (D^2+3D-10)y=20+5e^{3x} is y=c_{1}e^{2x}+c_{2}e^{-5x}-2+5/8 e^{3x}