What is the solution for (d^2y)/(dx^2)+10(dy)/(dx)+25y=0 ?

The solution for (d^2y)/(dx^2)+10(dy)/(dx)+25y=0 is y=c_{1}e^{-5x}+c_{2}xe^{-5x}

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(d^2y)/(dx^2)+10(dy)/(dx)+25y=0

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (y cos (x) y)

\frac{d}{d x} (sin (x^{2} y^{3}))

\frac{d}{d x} (lo g_{3} (x + 2))

y^{^{'}} = \frac{1}{e ^{- y} - x}

\int \frac{1}{( x - 2 ) ( x - 1 )} d x

What is the solution for (d^2y)/(dx^2)+10(dy)/(dx)+25y=0 ?
The solution for (d^2y)/(dx^2)+10(dy)/(dx)+25y=0 is y=c_{1}e^{-5x}+c_{2}xe^{-5x}