What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)-3y=5 ?

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

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(d^2y)/(dx^2)-2(dy)/(dx)-3y=5

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

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{5}{3}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{5}{3}

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{5}{3}

y^{^{''}} + y = sin (t), y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} - 8 y = 5 e^{- 3 x} - e^{- x}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} = x^{2}

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{e ^{- 2 x}}{x ^{2} + 1}

y^{^{''}} - 3 y^{^{'}} + 2 y = 5 e^{3 x}

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