What is the solution for (d^2y)/(dx^2)+9(dy)/(dx)+20y=0 ?

The solution for (d^2y)/(dx^2)+9(dy)/(dx)+20y=0 is y=c_{1}e^{-4x}+c_{2}e^{-5x}

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(d^2y)/(dx^2)+9(dy)/(dx)+20y=0

\frac{d ^{2} y}{d x ^{2}} + 9 \frac{d y}{d x} + 20 y = 0

y = c_{1} e^{- 4 x} + c_{2} e^{- 5 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 9 \frac{d y}{d x} + 20 y = 0

Solve linear ODE:

y = c_{1} e^{- 4 x} + c_{2} e^{- 5 x}

y = c_{1} e^{- 4 x} + c_{2} e^{- 5 x}

y^{^{''}} + 12 y^{^{'}} + 27 y = 0, y (0) = 11, y^{^{'}} (0) = - 81

y^{^{''}} + y^{^{'}} - 12 y = 0, y (0) = 4, y^{^{'}} (0) = - 9

4 y^{^{''}} - 4 y - 3 y = 0

\frac{d ^{2} x}{d t ^{2}} + 10 \frac{d x}{d t} + 25 x = 0

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 9, y^{^{'}} (0) = - 60

What is the solution for (d^2y)/(dx^2)+9(dy)/(dx)+20y=0 ?
The solution for (d^2y)/(dx^2)+9(dy)/(dx)+20y=0 is y=c_{1}e^{-4x}+c_{2}e^{-5x}