What is the solution for y^{''}+4y=0,y(pi)=0,y(0)=0 ?

The solution for y^{''}+4y=0,y(pi)=0,y(0)=0 is y=c_{2}sin(2t)

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

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

y = c_{2} sin (2 t)

Solution steps

y^{''} (t) + 4 y = 0

Solve linear ODE:

y = c_{2} sin (2 t)

y = c_{2} sin (2 t)

x^{^{''}} - 2 x^{^{'}} = 0

y^{^{''}} - 25 y^{^{'}} + 144 y = 0, y (0) = 2

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y^{^{'}} (0) = 14

x^{^{''}} + 2 x^{^{'}} - 8 x = 0

9 y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = 0

What is the solution for y^{''}+4y=0,y(pi)=0,y(0)=0 ?
The solution for y^{''}+4y=0,y(pi)=0,y(0)=0 is y=c_{2}sin(2t)