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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

- y^{^{''}} + y = e^{a \cdot x}, y (0) = 0, y (1) = 0

y^{^{''}} - 9 y = 9 e^{3} x - 6 x^{4}

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

y^{^{''}} - 3 y^{^{'}} - 4 y = sin (x)

y^{^{''}} + 4 y^{^{'}} + 32 y = 4 cos (4 t)

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