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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} - y^{^{''}} + y^{^{'}} - y = 2 e^{x}

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 11 t

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 12 t

y^{^{''}} + 3 y^{^{'}} = x^{2} e^{- 3 x}

y^{^{''}} + y = g

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