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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} + 3 y^{^{''}} - 18 y^{^{'}} - 40 y = 0

y^{^{''}} + 2 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 3

2 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 105 y = 0

6 y^{^{''''}} + 77 y^{^{''}} + 255 y = 0

y^{^{''}} - 0.28 y^{^{'}} - 0.006 y = 0

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