What is the solution for y^{''}+5*y^'+a*y=0,y(0)=1,y^'(0)=7 ?

The solution for y^{''}+5*y^'+a*y=0,y(0)=1,y^'(0)=7 is

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y^{''}+5y^'+ay=0,y(0)=1,y^'(0)=7

y^{^{''}} + 5 \cdot y^{^{'}} + a \cdot y = 0, y (0) = 1, y^{^{'}} (0) = 7

y = e^{\frac{t ( - 5 + 25 - 4 a )}{2}} (1 + \frac{- - 4 a + 25 + 19}{2 25 - 4 a}) - \frac{e ^{\frac{t ( - 5 - 25 - 4 a )}{2}} ( - - 4 a + 25 + 19 )}{2 25 - 4 a}

Solution steps

y^{''} (t) + 5 \cdot y^{'} (t) + a \cdot y = 0

Solve linear ODE:

y = e^{\frac{t ( - 5 + 25 - 4 a )}{2}} (1 + \frac{- - 4 a + 25 + 19}{2 25 - 4 a}) - \frac{e ^{\frac{t ( - 5 - 25 - 4 a )}{2}} ( - - 4 a + 25 + 19 )}{2 25 - 4 a}

y = e^{\frac{t ( - 5 + 25 - 4 a )}{2}} (1 + \frac{- - 4 a + 25 + 19}{2 25 - 4 a}) - \frac{e ^{\frac{t ( - 5 - 25 - 4 a )}{2}} ( - - 4 a + 25 + 19 )}{2 25 - 4 a}

5 y^{^{''}} + c y^{^{'}} + 45 y = 0, y (0) = - 8, y^{^{'}} (0) = 0

x^{^{''}} + 12 x^{^{'}} + 27 x = 0

(d^{5} - d^{3}) \cdot y = 0

y^{^{''}} - 16 y^{^{'}} + 64 y = 0, y (0) = 0, y^{^{'}} (0) = 9

y^{^{'''}} - 3 y^{^{''}} - y^{^{''}} + 3 y = 0

What is the solution for y^{''}+5*y^'+a*y=0,y(0)=1,y^'(0)=7 ?
The solution for y^{''}+5*y^'+a*y=0,y(0)=1,y^'(0)=7 is