What is the solution for 6y^{''}-7y^'-20y=0 ?

The solution for 6y^{''}-7y^'-20y=0 is y=c_{1}e^{(5t)/2}+c_{2}e^{-(4t)/3}

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6y^{''}-7y^'-20y=0

6 y^{^{''}} - 7 y^{^{'}} - 20 y = 0

y = c_{1} e^{\frac{5 t}{2}} + c_{2} e^{- \frac{4 t}{3}}

Solution steps

6 y^{''} (t) - 7 y^{'} (t) - 20 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{5 t}{2}} + c_{2} e^{- \frac{4 t}{3}}

y = c_{1} e^{\frac{5 t}{2}} + c_{2} e^{- \frac{4 t}{3}}

y^{^{''''}} + 49 y^{^{''}} = 0

y^{^{''''}} - 8 y^{^{'''}} + 23 y^{^{''}} - 28 y^{^{'}} + 12 y = 0

a (4 y^{^{''}} + y^{^{'}}) + 4 y^{^{'}} + y = 0

u^{^{'''}} + 3 u^{^{''}} - 2 H (t) = 0

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 25 y = 0

What is the solution for 6y^{''}-7y^'-20y=0 ?
The solution for 6y^{''}-7y^'-20y=0 is y=c_{1}e^{(5t)/2}+c_{2}e^{-(4t)/3}