What is the solution for 10(d^2y)/(dx^2)+20(dy)/(dx)+10y=0 ?

The solution for 10(d^2y)/(dx^2)+20(dy)/(dx)+10y=0 is y=c_{1}e^{-x}+c_{2}xe^{-x}

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10(d^2y)/(dx^2)+20(dy)/(dx)+10y=0

10 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 10 y = 0

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

Solution steps

10 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 10 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 3 y = 0, y (0) = 6, y^{^{'}} (0) = 2

x^{^{''}} + 5 x^{^{'}} = 0

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

\frac{d ^{2} y}{d x ^{2}} + 49 y = 0

y^{^{''''}} - 32 y^{^{'''}} + 256 y^{^{''}} = 0

What is the solution for 10(d^2y)/(dx^2)+20(dy)/(dx)+10y=0 ?
The solution for 10(d^2y)/(dx^2)+20(dy)/(dx)+10y=0 is y=c_{1}e^{-x}+c_{2}xe^{-x}