What is the solution for x^{''}+a*x=0 ?

The solution for x^{''}+a*x=0 is x=c_{1}cos(sqrt(a)t)+c_{2}sin(sqrt(a)t)

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x^{''}+a*x=0

x^{^{''}} + a \cdot x = 0

x = c_{1} cos (a t) + c_{2} sin (a t)

Solution steps

x^{''} (t) + a \cdot x = 0

Solve linear ODE:

x = c_{1} cos (a t) + c_{2} sin (a t)

x = c_{1} cos (a t) + c_{2} sin (a t)

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (1) = 0, y^{^{'}} (1) = 1

y^{^{''''}} + 3 y^{^{'''}} + 3 y^{^{''}} + y^{^{'}} = 0

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

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

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 5 y = 0

What is the solution for x^{''}+a*x=0 ?
The solution for x^{''}+a*x=0 is x=c_{1}cos(sqrt(a)t)+c_{2}sin(sqrt(a)t)