What is the solution for 3y^{''}+15y=0 ?

The solution for 3y^{''}+15y=0 is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)

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3y^{''}+15y=0

3 y^{^{''}} + 15 y = 0

y = c_{1} cos (5 t) + c_{2} sin (5 t)

Solution steps

3 y^{''} (t) + 15 y = 0

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t)

y^{^{''}} + (2 a - 5) y^{^{'}} + a (a - 5) y = 0

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

\frac{1}{4} x^{^{''}} + 10 x^{^{'}} + 1000 x = 0

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

4 y^{^{'''}} - 7 y^{^{''}} - 34 y^{^{'}} - 8 y = 0

What is the solution for 3y^{''}+15y=0 ?
The solution for 3y^{''}+15y=0 is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)