What is the solution for y^{''}+0.75y=0 ?

The solution for y^{''}+0.75y=0 is y=c_{1}cos((sqrt(3)t)/2)+c_{2}sin((sqrt(3)t)/2)

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y^{''}+0.75y=0

y^{^{''}} + 0.75 y = 0

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

Solution steps

y^{''} (t) + 0.75 y = 0

Solve linear ODE:

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

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

\frac{3}{2} y^{^{''}} + 3 y^{^{'}} + 15 y = 0

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = - 1, y (1) = 2

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

(D^{5} - D^{3}) y = 0

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

What is the solution for y^{''}+0.75y=0 ?
The solution for y^{''}+0.75y=0 is y=c_{1}cos((sqrt(3)t)/2)+c_{2}sin((sqrt(3)t)/2)