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

The solution for y^{''}-3y^'+5y=0 is y=e^{(3t)/2}(c_{1}cos((sqrt(11)t)/2)+c_{2}sin((sqrt(11)t)/2))

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

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

y = e^{\frac{3 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2}))

Solution steps

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

Solve linear ODE:

y = e^{\frac{3 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2}))

y = e^{\frac{3 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2}))

y^{^{''}} + 2 y^{^{'}} + 36 y = 0

x^{3} y^{^{''}} + 2 x^{3} y^{^{'}} + x^{3} y = 0

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

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

y^{^{''}} + 4 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 2

What is the solution for y^{''}-3y^'+5y=0 ?
The solution for y^{''}-3y^'+5y=0 is y=e^{(3t)/2}(c_{1}cos((sqrt(11)t)/2)+c_{2}sin((sqrt(11)t)/2))