What is the solution for 4y^{''}+8y^'-21y=0,y(0)=1,y^'(0)=0 ?

The solution for 4y^{''}+8y^'-21y=0,y(0)=1,y^'(0)=0 is y=(1-3/10)e^{(3t)/2}+3/10 e^{-(7t)/2}

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4y^{''}+8y^'-21y=0,y(0)=1,y^'(0)=0

4 y^{^{''}} + 8 y^{^{'}} - 21 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = (1 - \frac{3}{10}) e^{\frac{3 t}{2}} + \frac{3}{10} e^{- \frac{7 t}{2}}

Solution steps

4 y^{''} (t) + 8 y^{'} (t) - 21 y = 0

Solve linear ODE:

y = (1 - \frac{3}{10}) e^{\frac{3 t}{2}} + \frac{3}{10} e^{- \frac{7 t}{2}}

y = (1 - \frac{3}{10}) e^{\frac{3 t}{2}} + \frac{3}{10} e^{- \frac{7 t}{2}}

u^{^{''}} + 7 H (t) + 2 H (t) = 0

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = α, y^{^{'}} (0) = 5

y^{^{''}} + 49 y = 0

x^{^{''}} + a x^{^{'}} + 2^{2} x = 0

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

What is the solution for 4y^{''}+8y^'-21y=0,y(0)=1,y^'(0)=0 ?
The solution for 4y^{''}+8y^'-21y=0,y(0)=1,y^'(0)=0 is y=(1-3/10)e^{(3t)/2}+3/10 e^{-(7t)/2}