What is the solution for 12y^{''}-5y^'-3y=0 ?

The solution for 12y^{''}-5y^'-3y=0 is y=c_{1}e^{(3t)/4}+c_{2}e^{-t/3}

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12y^{''}-5y^'-3y=0

12 y^{^{''}} - 5 y^{^{'}} - 3 y = 0

y = c_{1} e^{\frac{3 t}{4}} + c_{2} e^{- \frac{t}{3}}

Solution steps

12 y^{''} (t) - 5 y^{'} (t) - 3 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{3 t}{4}} + c_{2} e^{- \frac{t}{3}}

y = c_{1} e^{\frac{3 t}{4}} + c_{2} e^{- \frac{t}{3}}

What is the solution for 12y^{''}-5y^'-3y=0 ?
The solution for 12y^{''}-5y^'-3y=0 is y=c_{1}e^{(3t)/4}+c_{2}e^{-t/3}