What is the solution for y^{''}+b*y=0,y(0)-9y^'(0)=0,y^'(9)=0 ?

The solution for y^{''}+b*y=0,y(0)-9y^'(0)=0,y^'(9)=0 is y=c_{1}cos(sqrt(b)t)+c_{2}sin(sqrt(b)t)

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y^{''}+b*y=0,y(0)-9y^'(0)=0,y^'(9)=0

y^{^{''}} + b \cdot y = 0, y (0) - 9 y^{^{'}} (0) = 0, y^{^{'}} (9) = 0

y = c_{1} cos (b t) + c_{2} sin (b t)

Solution steps

y^{''} (t) + b \cdot y = 0

Solve linear ODE:

y = c_{1} cos (b t) + c_{2} sin (b t)

y = c_{1} cos (b t) + c_{2} sin (b t)

y^{^{'''}} + 6 y^{^{''}} + 9 y^{^{'}} + 4 y = 0

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = 6, y^{^{'}} (0) = 2

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} = 0

y^{^{''}} + 0.8 y^{^{'}} + 100 y = 0, y (0) = 0, y^{^{'}} (0) = 4

18 y^{^{''}} + 72 y = 0

What is the solution for y^{''}+b*y=0,y(0)-9y^'(0)=0,y^'(9)=0 ?
The solution for y^{''}+b*y=0,y(0)-9y^'(0)=0,y^'(9)=0 is y=c_{1}cos(sqrt(b)t)+c_{2}sin(sqrt(b)t)