What is the solution for (d^2y)/(dx^2)+3y^'+2=0 ?

The solution for (d^2y)/(dx^2)+3y^'+2=0 is y=c_{1}+c_{2}e^{-3x}-(2x)/3

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(d^2y)/(dx^2)+3y^'+2=0

\frac{d ^{2} y}{d x ^{2}} + 3 y^{^{'}} + 2 = 0

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

Solution steps

y^{''} (x) + 3 y^{'} (x) + 2 = 0

Solve linear ODE:

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

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

(D^{2} - 2 D - 3) y = e^{3 x} + cos (x)

y^{^{''}} + 3 y^{^{'}} + 7 y = cos (t), y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0, y (0) = 0

4 y^{^{''}} + 4 y^{^{'}} + 1 = 0

D (x) = a - 2

What is the solution for (d^2y)/(dx^2)+3y^'+2=0 ?
The solution for (d^2y)/(dx^2)+3y^'+2=0 is y=c_{1}+c_{2}e^{-3x}-(2x)/3