What is the solution for (d^2y)/(dx^2)-7(dy)/(dx)+6y=e^x ?

The solution for (d^2y)/(dx^2)-7(dy)/(dx)+6y=e^x is y=c_{1}e^{6x}+c_{2}e^x-(e^xx)/5

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(d^2y)/(dx^2)-7(dy)/(dx)+6y=e^x

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 6 y = e^{x}

y = c_{1} e^{6 x} + c_{2} e^{x} - \frac{e ^{x} x}{5}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 6 y = e^{x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{x} - \frac{e ^{x} x}{5}

y = c_{1} e^{6 x} + c_{2} e^{x} - \frac{e ^{x} x}{5}

y^{^{''}} + y = 12 cos^{2} (x)

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

x^{^{''}} + 3 x^{^{'}} + 33 x = 10 cos (5 t)

y^{^{''}} + 4 y^{^{'}} + 3 y = 5 e^{- 3 t}

y^{^{'''}} - 2 y^{^{''}} + 5 y^{^{'}} = e^{x} cos (2 x)

What is the solution for (d^2y)/(dx^2)-7(dy)/(dx)+6y=e^x ?
The solution for (d^2y)/(dx^2)-7(dy)/(dx)+6y=e^x is y=c_{1}e^{6x}+c_{2}e^x-(e^xx)/5