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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 5 y^{^{'}} + 6 y = x

\frac{1}{6} y^{^{''}} + 6 y = 3 tan (6 t) - \frac{1}{3} e^{t}

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

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{2 t}, y (0) = 0, y^{^{'}} (0) = 0

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

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