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

The solution for y^{''}-y^'-5y=0 is y=c_{1}e^{((1+sqrt(21))t)/2}+c_{2}e^{((1-sqrt(21))t)/2}

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

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

y = c_{1} e^{\frac{( 1 + 21 ) t}{2}} + c_{2} e^{\frac{( 1 - 21 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( 1 + 21 ) t}{2}} + c_{2} e^{\frac{( 1 - 21 ) t}{2}}

y = c_{1} e^{\frac{( 1 + 21 ) t}{2}} + c_{2} e^{\frac{( 1 - 21 ) t}{2}}

\frac{5}{8} x^{^{''}} + 80 x = 0

\frac{d ^{2} x}{d t ^{2}} = - 4 x

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 12 y = 0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 37 y = 0

25 x^{^{''}} + 50 x^{^{'}} + 169 x = 0, x (0) = 3, x^{^{'}} (0) = 14

What is the solution for y^{''}-y^'-5y=0 ?
The solution for y^{''}-y^'-5y=0 is y=c_{1}e^{((1+sqrt(21))t)/2}+c_{2}e^{((1-sqrt(21))t)/2}