What is the solution for 4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9 ?

The solution for 4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9 is y=(1+15/4)e^{(3t)/2}-15/4 e^{-t/2}

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4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 9

y = (1 + \frac{15}{4}) e^{\frac{3 t}{2}} - \frac{15}{4} e^{- \frac{t}{2}}

Solution steps

4 y^{''} (t) - 4 y^{'} (t) - 3 y = 0

Solve linear ODE:

y = (1 + \frac{15}{4}) e^{\frac{3 t}{2}} - \frac{15}{4} e^{- \frac{t}{2}}

y = (1 + \frac{15}{4}) e^{\frac{3 t}{2}} - \frac{15}{4} e^{- \frac{t}{2}}

y^{^{''}} - 5 y^{^{'}} - 36 y = 0

y^{^{''}} + y = 0, y^{^{'}} (\frac{π}{2}) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} - 2 y = 0

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 4, y^{^{'}} (0) = - 2

3 y^{^{''}} = 5 y^{^{'}}

What is the solution for 4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9 ?
The solution for 4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9 is y=(1+15/4)e^{(3t)/2}-15/4 e^{-t/2}