What is the solution for 4*y^{''}-11*y^'-3y=5*e^{3x} ?

The solution for 4*y^{''}-11*y^'-3y=5*e^{3x} is y=c_{1}e^{3x}+c_{2}e^{-x/4}+(5e^{3x}x)/(13)

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4y^{''}-11y^'-3y=5*e^{3x}

4 \cdot y^{^{''}} - 11 \cdot y^{^{'}} - 3 y = 5 \cdot e^{3 x}

y = c_{1} e^{3 x} + c_{2} e^{- \frac{x}{4}} + \frac{5 e ^{3 x} x}{13}

Solution steps

4 \cdot y^{''} (x) - 11 \cdot y^{'} (x) - 3 y = 5 \cdot e^{3 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- \frac{x}{4}} + \frac{5 e ^{3 x} x}{13}

y = c_{1} e^{3 x} + c_{2} e^{- \frac{x}{4}} + \frac{5 e ^{3 x} x}{13}

\frac{d ^{2} x}{d t ^{2}} + x = 6 cos (2 t), x (0) = 3

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

y^{^{''}} - 12 y^{^{'}} + 36 y = 30 x + 4

y^{^{''}} - y^{^{'}} = 5

y^{^{''}} - y^{^{'}} = 2

What is the solution for 4*y^{''}-11*y^'-3y=5*e^{3x} ?
The solution for 4*y^{''}-11*y^'-3y=5*e^{3x} is y=c_{1}e^{3x}+c_{2}e^{-x/4}+(5e^{3x}x)/(13)