What is the solution for y^{''}+ay=0,y(0)=0,y(1)=0 ?

The solution for y^{''}+ay=0,y(0)=0,y(1)=0 is y=0*sin(sqrt(a)t)

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

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

(D^{3} + D^{2} + D + 1) y = 0

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (1) = 1, y^{^{'}} (1) = 0

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

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

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 6, y^{^{'}} (0) = 2

What is the solution for y^{''}+ay=0,y(0)=0,y(1)=0 ?
The solution for y^{''}+ay=0,y(0)=0,y(1)=0 is y=0*sin(sqrt(a)t)