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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} - 6 y = 5 x e^{3 x}

y^{^{''}} - 6 y + 9 y = t^{2} e^{3 t}

y^{^{''}} - 12 y^{^{'}} + 36 y = 14 e^{6 x}

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

y^{^{'''}} - y^{^{''}} - 25 y^{^{'}} + 25 y = 4 - e^{x} + e^{5 x}

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