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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x^{^{'''}} + 4 x^{^{''}} + 13 x^{^{'}} = 0

(d^{4} - 5 d^{3} + 5 d^{2} + 5 d - 6) y = 0

14 y^{^{''''}} + 95 y^{^{''}} + 144 y = 0

y^{^{''}} = 5 y

5 \frac{d ^{2} x}{d t ^{2}} + 3 \frac{d x}{d t} + 6 x = 0, x (0) = 2

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