What is the solution for ay^{''}+by=0 ?

The solution for ay^{''}+by=0 is y=c_{1}cos(sqrt(b/a)t)+c_{2}sin(sqrt(b/a)t)

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ay^{''}+by=0

a y^{^{''}} + b y = 0

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

Solution steps

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

Solve linear ODE:

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

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

sin (\frac{π x}{2})

2 sin (3 x)

\int \frac{sin ( \frac{1}{x ^{3}} )}{x ^{4}} d x

\frac{\partial}{\partial x} (\frac{( 4 x - 4 y )}{4 x + 4 y})

\frac{\partial}{\partial x} (tan (8 + 2 x^{2} y^{4} z^{2}))

What is the solution for ay^{''}+by=0 ?
The solution for ay^{''}+by=0 is y=c_{1}cos(sqrt(b/a)t)+c_{2}sin(sqrt(b/a)t)