What is the solution for 4y^{''}-y^'-3y=0,y(0)=9,y^'(0)=0.25 ?

The solution for 4y^{''}-y^'-3y=0,y(0)=9,y^'(0)=0.25 is y=4e^t+5e^{-(3t)/4}

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4y^{''}-y^'-3y=0,y(0)=9,y^'(0)=0.25

4 y^{^{''}} - y^{^{'}} - 3 y = 0, y (0) = 9, y^{^{'}} (0) = 0.25

y = 4 e^{t} + 5 e^{- \frac{3 t}{4}}

Solution steps

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

Solve linear ODE:

y = 4 e^{t} + 5 e^{- \frac{3 t}{4}}

y = 4 e^{t} + 5 e^{- \frac{3 t}{4}}

What is the solution for 4y^{''}-y^'-3y=0,y(0)=9,y^'(0)=0.25 ?
The solution for 4y^{''}-y^'-3y=0,y(0)=9,y^'(0)=0.25 is y=4e^t+5e^{-(3t)/4}