What is the solution for 4y^{''}-4y^'-3y=0,y(0)=0,y^'(0)=10 ?

The solution for 4y^{''}-4y^'-3y=0,y(0)=0,y^'(0)=10 is y=5e^{(3t)/2}-5e^{-t/2}

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

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

y = 5 e^{\frac{3 t}{2}} - 5 e^{- \frac{t}{2}}

Solution steps

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

Solve linear ODE:

y = 5 e^{\frac{3 t}{2}} - 5 e^{- \frac{t}{2}}

y = 5 e^{\frac{3 t}{2}} - 5 e^{- \frac{t}{2}}

y^{^{''}} + 4 y^{^{'}} + 29 y = 0, y (0) = 4, y^{^{'}} (0) = - 5

y + 2 y^{^{'''}} + 10 y^{^{''}} + 18 y^{^{'}} + 9 y = 0

y^{^{''}} + 16 y = 0, y (0) = 1, y^{^{'}} (1) = 0

y^{^{''}} + 16 y = 0, y (0) = 1, y (1) = 0

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

What is the solution for 4y^{''}-4y^'-3y=0,y(0)=0,y^'(0)=10 ?
The solution for 4y^{''}-4y^'-3y=0,y(0)=0,y^'(0)=10 is y=5e^{(3t)/2}-5e^{-t/2}