What is the solution for y^{''}+10y^'+21y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+10y^'+21y=0,y(0)=1,y^'(0)=0 is y=(1+3/4)e^{-3t}-3/4 e^{-7t}

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y^{''}+10y^'+21y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 10 y^{^{'}} + 21 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = (1 + \frac{3}{4}) e^{- 3 t} - \frac{3}{4} e^{- 7 t}

Solution steps

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

Solve linear ODE:

y = (1 + \frac{3}{4}) e^{- 3 t} - \frac{3}{4} e^{- 7 t}

y = (1 + \frac{3}{4}) e^{- 3 t} - \frac{3}{4} e^{- 7 t}

y^{^{''}} + y^{^{'}} + 9.25 y = 0, y^{^{'}} (0) = 8

x^{^{''}} + 9 x = 0, x (0) = 1

y^{^{''''}} - 4 y^{^{'''}} + 20 y^{^{''}} - 64 y^{^{'}} + 64 y = 0

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 5 x = 0, x (0) = 1

9 y^{^{''}} + 8 y^{^{'}} + 7 y = 0

What is the solution for y^{''}+10y^'+21y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+10y^'+21y=0,y(0)=1,y^'(0)=0 is y=(1+3/4)e^{-3t}-3/4 e^{-7t}