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)

9 y^{^{''}} + 36 y^{^{'}} + 100 y = 0, y (0) = 4, y^{^{'}} (0) = 9

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

\frac{d ^{2} y}{d t ^{2}} - 6 \frac{d y}{d t} - 7 y = 0

x^{^{''}} = - 2 x

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

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)