What is the solution for y^{''}+(a^2)y=0 ?

The solution for y^{''}+(a^2)y=0 is y=c_{1}cos(at)+c_{2}sin(at)

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y^{''}+(a^2)y=0

y^{^{''}} + (a^{2}) y = 0

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

Solution steps

y^{''} (t) + (a^{2}) y = 0

Solve linear ODE:

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

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

y^{^{''}} = k y (x)

4 \frac{d ^{2} x}{d t ^{2}} + c \frac{d x}{d t} + k (x) = 0

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 34 y = 0

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 4, y^{^{'}} (0) = 18

6 y^{^{''}} + 108 y^{^{'}} + 486 y = 0

What is the solution for y^{''}+(a^2)y=0 ?
The solution for y^{''}+(a^2)y=0 is y=c_{1}cos(at)+c_{2}sin(at)