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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - 1 = 0

y^{^{''}} + 9 y = 6 cot (3 t) cos (3 t)

2 y^{^{''}} - 3 y^{^{'}} = 9 x^{2} + 10, y (0) = 1, y^{^{'}} (0) = - 3

x^{^{''}} + 2 x^{^{'}} + x = 3 cos (t)

y^{^{''}} + 2 y^{^{'}} + 4 y = 5 sin (3 t)

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