What is the solution for 18y^{''}+3y^'-10y=0 ?

The solution for 18y^{''}+3y^'-10y=0 is y=c_{1}e^{(2t)/3}+c_{2}e^{-(5t)/6}

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18y^{''}+3y^'-10y=0

18 y^{^{''}} + 3 y^{^{'}} - 10 y = 0

y = c_{1} e^{\frac{2 t}{3}} + c_{2} e^{- \frac{5 t}{6}}

Solution steps

18 y^{''} (t) + 3 y^{'} (t) - 10 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{2 t}{3}} + c_{2} e^{- \frac{5 t}{6}}

y = c_{1} e^{\frac{2 t}{3}} + c_{2} e^{- \frac{5 t}{6}}

What is the solution for 18y^{''}+3y^'-10y=0 ?
The solution for 18y^{''}+3y^'-10y=0 is y=c_{1}e^{(2t)/3}+c_{2}e^{-(5t)/6}