What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=4e^{2x} ?

The solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=4e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}-4xe^{2x}

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(d^2y)/(dx^2)-5(dy)/(dx)+6y=4e^{2x}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 4 e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} - 4 x e^{2 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 4 e^{2 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} - 4 x e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} - 4 x e^{2 x}

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

11 x^{^{''}} + 112.5 x = 5 e^{- t}, x (0) = 0, x^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} + 2 y = 6 e^{- t}, y (0) = 1, y^{^{'}} (0) = 2

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

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + 5 = 0

What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=4e^{2x} ?
The solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=4e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}-4xe^{2x}