What is the solution for y^{''}+ay=0,y(0)=0,y^'(0)=0 ?

The solution for y^{''}+ay=0,y(0)=0,y^'(0)=0 is y=0*sin(sqrt(a)t)

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y^{''}+ay=0,y(0)=0,y^'(0)=0

y^{^{''}} + a y = 0, y (0) = 0, y^{^{'}} (0) = 0

y = 0 \cdot sin (a t)

Solution steps

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

Solve linear ODE:

y = 0 \cdot sin (a t)

y = 0 \cdot sin (a t)

\frac{1}{4} x^{^{''}} - x = 0, x (0) = 1, x^{^{'}} (0) = 5

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

4 x^{^{''}} + 15 x^{^{'}} + 14 x = 0

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 0, y (0) = 3, y^{^{'}} (0) = - 1

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

What is the solution for y^{''}+ay=0,y(0)=0,y^'(0)=0 ?
The solution for y^{''}+ay=0,y(0)=0,y^'(0)=0 is y=0*sin(sqrt(a)t)