What is the solution for (d^2y)/(dx^2)+7(dy)/(dx)+10y=0 ?

The solution for (d^2y)/(dx^2)+7(dy)/(dx)+10y=0 is y=c_{1}e^{-2x}+c_{2}e^{-5x}

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(d^2y)/(dx^2)+7(dy)/(dx)+10y=0

\frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} + 10 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} + 10 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 8 y^{^{'}} - 65 y = 0

\frac{d ^{2} x}{d t ^{2}} + 3 \frac{d x}{d t} + 7 x = 0

y^{^{''}} + (y^{^{'}}) + y = 0

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = 2

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

What is the solution for (d^2y)/(dx^2)+7(dy)/(dx)+10y=0 ?
The solution for (d^2y)/(dx^2)+7(dy)/(dx)+10y=0 is y=c_{1}e^{-2x}+c_{2}e^{-5x}