What is the solution for 3y^{''}+8y^'-3y=0,y(0)=4,y^'(0)=-2 ?

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

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3y^{''}+8y^'-3y=0,y(0)=4,y^'(0)=-2

3 y^{^{''}} + 8 y^{^{'}} - 3 y = 0, y (0) = 4, y^{^{'}} (0) = - 2

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

Solution steps

3 y^{''} (t) + 8 y^{'} (t) - 3 y = 0

Solve linear ODE:

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

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

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