What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)-3y=6 ?

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

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(d^2y)/(dx^2)+2(dy)/(dx)-3y=6

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 6

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 6

Solve linear ODE:

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

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

y^{^{''}} + y = 10

4 y^{^{''}} + y = e^{- 2 t} cos (\frac{t}{2}) + 6 t sin (\frac{t}{2})

y^{^{''''}} - 2 y^{^{'''}} + y^{^{''}} = t^{3}

y^{^{''}} - y - x = 0

(D^{2} + 2) y = e^{x + 2}

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