What is the solution for (d^2y)/(dx^2)+5(dy)/(dx)+6=0 ?

The solution for (d^2y)/(dx^2)+5(dy)/(dx)+6=0 is y=c_{1}+c_{2}e^{-5x}-(6x)/5

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(d^2y)/(dx^2)+5(dy)/(dx)+6=0

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 = 0

y = c_{1} + c_{2} e^{- 5 x} - \frac{6 x}{5}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- 5 x} - \frac{6 x}{5}

y = c_{1} + c_{2} e^{- 5 x} - \frac{6 x}{5}

y^{^{'''}} - y = 1

y^{^{''}} + 7 y^{^{'}} + 12 y = 4 e^{5 t}, y (0) = 2, y^{^{'}} (0) = 0

100 y^{^{''}} - 60 y^{^{'}} + 13 y + 30 = 0

y^{^{''}} - 2 y^{^{'}} - 8 y = 2 e^{4 x} + 3 x e^{2 x} + 4 x

y^{^{''}} + 16 y = 4 sin (2 x)

What is the solution for (d^2y)/(dx^2)+5(dy)/(dx)+6=0 ?
The solution for (d^2y)/(dx^2)+5(dy)/(dx)+6=0 is y=c_{1}+c_{2}e^{-5x}-(6x)/5