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

The solution for y^{''}+2y^'-3y=2e^x-10sin(x) is y=c_{1}e^x+c_{2}e^{-3x}+(e^xx)/2+2sin(x)+cos(x)

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y^{''}+2y^'-3y=2e^x-10sin(x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 2 e^{x} - 10 sin (x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} + \frac{e ^{x} x}{2} + 2 sin (x) + cos (x)

Solution steps

y^{''} (x) + 2 y^{'} (x) - 3 y = 2 e^{x} - 10 sin (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} + \frac{e ^{x} x}{2} + 2 sin (x) + cos (x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} + \frac{e ^{x} x}{2} + 2 sin (x) + cos (x)

y^{^{''}} - 3 y^{^{'}} - 4 y = 8 e^{t} cos (2 t)

3 y^{^{''}} + 27 y = 2 cos (4 x)

y^{^{'''}} - 3 y^{^{''}} + 4 y^{^{'}} - 12 y = 13 e^{3 x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 2 y = 2 (x + 1)^{2}

y^{^{''}} + 3 y + 2 y = t

What is the solution for y^{''}+2y^'-3y=2e^x-10sin(x) ?
The solution for y^{''}+2y^'-3y=2e^x-10sin(x) is y=c_{1}e^x+c_{2}e^{-3x}+(e^xx)/2+2sin(x)+cos(x)