What is the solution for y^{''}+49y=0,y(pi)=0,y(0)=0 ?

The solution for y^{''}+49y=0,y(pi)=0,y(0)=0 is y=c_{2}sin(7t)

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y^{''}+49y=0,y(pi)=0,y(0)=0

y^{^{''}} + 49 y = 0, y (π) = 0, y (0) = 0

y = c_{2} sin (7 t)

Solution steps

y^{''} (t) + 49 y = 0

Solve linear ODE:

y = c_{2} sin (7 t)

y = c_{2} sin (7 t)

\frac{d ^{2} y}{d x ^{2}} + a y = 0

\frac{d ^{2} y}{d x ^{2}} + 5 y = 0

4 y^{^{''}} + 20 y^{^{'}} + 169 y = 0, y (0) = 3, y^{^{'}} (0) = 1

4 y^{^{''}} - 10 y^{^{'}} = 0

y^{^{'''}} + 4 y^{^{''}} - 12 y^{^{'}} = 0

What is the solution for y^{''}+49y=0,y(pi)=0,y(0)=0 ?
The solution for y^{''}+49y=0,y(pi)=0,y(0)=0 is y=c_{2}sin(7t)