What is the solution for x^{''}+10x^'+21x=0 ?

The solution for x^{''}+10x^'+21x=0 is x=c_{1}e^{-3t}+c_{2}e^{-7t}

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x^{''}+10x^'+21x=0

x^{^{''}} + 10 x^{^{'}} + 21 x = 0

x = c_{1} e^{- 3 t} + c_{2} e^{- 7 t}

Solution steps

x^{''} (t) + 10 x^{'} (t) + 21 x = 0

Solve linear ODE:

x = c_{1} e^{- 3 t} + c_{2} e^{- 7 t}

x = c_{1} e^{- 3 t} + c_{2} e^{- 7 t}

\int \frac{x + 10}{x ^{2} - x - 2} d x

\int_{- 3}^{0} (9 - x^{2}) d x

\frac{\partial}{\partial x} (7 y^{6} x^{6} - 6 y^{5} x^{5})

y d x + (x - 4) d y = 0

\frac{d}{d x} (e^{x^{- 2}})

What is the solution for x^{''}+10x^'+21x=0 ?
The solution for x^{''}+10x^'+21x=0 is x=c_{1}e^{-3t}+c_{2}e^{-7t}