What is the solution for 3y^{''}-5y^'-14y=0 ?

The solution for 3y^{''}-5y^'-14y=0 is y=c_{1}e^{((5+sqrt(193))t)/6}+c_{2}e^{((5-sqrt(193))t)/6}

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3y^{''}-5y^'-14y=0

3 y^{^{''}} - 5 y^{^{'}} - 14 y = 0

y = c_{1} e^{\frac{( 5 + 193 ) t}{6}} + c_{2} e^{\frac{( 5 - 193 ) t}{6}}

Solution steps

3 y^{''} (t) - 5 y^{'} (t) - 14 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( 5 + 193 ) t}{6}} + c_{2} e^{\frac{( 5 - 193 ) t}{6}}

y = c_{1} e^{\frac{( 5 + 193 ) t}{6}} + c_{2} e^{\frac{( 5 - 193 ) t}{6}}

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What is the solution for 3y^{''}-5y^'-14y=0 ?
The solution for 3y^{''}-5y^'-14y=0 is y=c_{1}e^{((5+sqrt(193))t)/6}+c_{2}e^{((5-sqrt(193))t)/6}