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

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

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

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

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 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}

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

\int \frac{1}{9 e ^{y} + e ^{- y}} d y

\frac{d}{d x} (\frac{5 x ^{2}}{sin ( x )})

n = 1 \sum \infty \frac{2 ^{n}}{n ^{3}}

\frac{d}{d x} (x^{2} + 10 x + 25)

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