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

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

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(d^2y)/(dx^2)-4(dy)/(dx)+3y=e^{4x}

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 3 y = e^{4 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 3 y = e^{4 x}

Solve linear ODE:

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

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

y^{^{''}} + 8 y^{^{'}} - 9 y = 64 x + 1

\frac{d ^{2} y}{d x ^{2}} + y = 3 e^{- 5 x}

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

y^{^{''}} - 6 y^{^{'}} + 13 y = e^{3 x} cos (2 x)

y = 5 \frac{d ^{2} x}{d y ^{2}} + 3 \frac{d x}{d y}

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