What is the solution for a(d^2y)/(dx^2)+yb^2=0 ?

The solution for a(d^2y)/(dx^2)+yb^2=0 is y=c_{1}cos((bx)/(sqrt(a)))+c_{2}sin((bx)/(sqrt(a)))

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a(d^2y)/(dx^2)+yb^2=0

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

y = c_{1} cos (\frac{b x}{a}) + c_{2} sin (\frac{b x}{a})

Solution steps

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

Solve linear ODE:

y = c_{1} cos (\frac{b x}{a}) + c_{2} sin (\frac{b x}{a})

y = c_{1} cos (\frac{b x}{a}) + c_{2} sin (\frac{b x}{a})

y^{^{''}} + \frac{48}{2} y = 0

y^{^{''}} - y^{^{'}} + 0.25 y = 0, y (0) = 2, y^{^{'}} (0) = 2

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

2 y^{^{''}} + 10 y^{^{'}} + 8 y = 0, y^{^{'}} (0) = 0, y (0) = 5

2 y^{^{''}} - 4 y^{^{'}} + 5 y = 0

What is the solution for a(d^2y)/(dx^2)+yb^2=0 ?
The solution for a(d^2y)/(dx^2)+yb^2=0 is y=c_{1}cos((bx)/(sqrt(a)))+c_{2}sin((bx)/(sqrt(a)))