What is the solution for 3y^{''}-10y^'-13y=13x-3 ?

The solution for 3y^{''}-10y^'-13y=13x-3 is y=c_{1}e^{(13x)/3}+c_{2}e^{-x}-x+1

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3y^{''}-10y^'-13y=13x-3

3 y^{^{''}} - 10 y^{^{'}} - 13 y = 13 x - 3

y = c_{1} e^{\frac{13 x}{3}} + c_{2} e^{- x} - x + 1

Solution steps

3 y^{''} (x) - 10 y^{'} (x) - 13 y = 13 x - 3

Solve linear ODE:

y = c_{1} e^{\frac{13 x}{3}} + c_{2} e^{- x} - x + 1

y = c_{1} e^{\frac{13 x}{3}} + c_{2} e^{- x} - x + 1

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

y^{^{'''}} + 25 y^{^{'}} = 10 sin (5 x) - 4 x^{2}

y^{^{''}} + 4 y^{^{'}} + 8 y = e^{2 x} (sin (2 x) + cos (2 x))

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

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

What is the solution for 3y^{''}-10y^'-13y=13x-3 ?
The solution for 3y^{''}-10y^'-13y=13x-3 is y=c_{1}e^{(13x)/3}+c_{2}e^{-x}-x+1