What is the solution for 3y^{''}-4y^'-15y=0,y(0)=-7,y^'(0)=-2 ?

The solution for 3y^{''}-4y^'-15y=0,y(0)=-7,y^'(0)=-2 is y=(-7+57/14)e^{3t}-57/14 e^{-(5t)/3}

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3y^{''}-4y^'-15y=0,y(0)=-7,y^'(0)=-2

3 y^{^{''}} - 4 y^{^{'}} - 15 y = 0, y (0) = - 7, y^{^{'}} (0) = - 2

y = (- 7 + \frac{57}{14}) e^{3 t} - \frac{57}{14} e^{- \frac{5 t}{3}}

Solution steps

3 y^{''} (t) - 4 y^{'} (t) - 15 y = 0

Solve linear ODE:

y = (- 7 + \frac{57}{14}) e^{3 t} - \frac{57}{14} e^{- \frac{5 t}{3}}

y = (- 7 + \frac{57}{14}) e^{3 t} - \frac{57}{14} e^{- \frac{5 t}{3}}

What is the solution for 3y^{''}-4y^'-15y=0,y(0)=-7,y^'(0)=-2 ?
The solution for 3y^{''}-4y^'-15y=0,y(0)=-7,y^'(0)=-2 is y=(-7+57/14)e^{3t}-57/14 e^{-(5t)/3}