What is the solution for y^{''}-1/2 y^'+5y=0 ?

The solution for y^{''}-1/2 y^'+5y=0 is y=e^{t/4}(c_{1}cos((sqrt(79)t)/4)+c_{2}sin((sqrt(79)t)/4))

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y^{''}-1/2 y^'+5y=0

y^{^{''}} - \frac{1}{2} y^{^{'}} + 5 y = 0

y = e^{\frac{t}{4}} (c_{1} cos (\frac{79 t}{4}) + c_{2} sin (\frac{79 t}{4}))

Solution steps

y^{''} (t) - \frac{1}{2} y^{'} (t) + 5 y = 0

Solve linear ODE:

y = e^{\frac{t}{4}} (c_{1} cos (\frac{79 t}{4}) + c_{2} sin (\frac{79 t}{4}))

y = e^{\frac{t}{4}} (c_{1} cos (\frac{79 t}{4}) + c_{2} sin (\frac{79 t}{4}))

x^{^{''}} + 8 x = 0

\frac{y}{y ^{^{''}}} = 2, y^{^{'}} (0) = 6, y (0) = 0

y^{^{'''}} + 3 y^{^{''}} - 10 y^{^{'}} - 24 y = 0

y^{^{''}} + 16 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + y^{^{'}} - 56 y = 0, y (0) = 5, y^{^{'}} (0) = 5

What is the solution for y^{''}-1/2 y^'+5y=0 ?
The solution for y^{''}-1/2 y^'+5y=0 is y=e^{t/4}(c_{1}cos((sqrt(79)t)/4)+c_{2}sin((sqrt(79)t)/4))