What is the solution for (d^2y)/(dx^2)(1)+(dy)/(dx)(5)+4y=0 ?

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

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(d^2y)/(dx^2)(1)+(dy)/(dx)(5)+4y=0

\frac{d ^{2} y}{d x ^{2}} (1) + \frac{d y}{d x} (5) + 4 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} (1) + \frac{d y}{d x} (5) + 4 y = 0

Solve linear ODE:

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

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

2 y^{^{''}} - 3 y^{^{'}} - 6 y = 0

9 x^{^{''}} - 12 x^{^{'}} + 4 x = 0, x (0) = 1, x^{^{'}} (0) = - 1

y^{^{''}} + y = 0, y^{^{'}} = 5, y (0) = 9

y^{^{''}} = 7 y^{^{'}} + 4 y

y^{^{''}} + 0.05 y^{^{'}} + 25 y = 0

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