What is the solution for y^{''}+a^2*n^2*pi^2*y=0 ?

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

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y^{''}+a^2n^2pi^2*y=0

y^{^{''}} + a^{2} \cdot n^{2} \cdot π^{2} \cdot y = 0

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

Solution steps

y^{''} (t) + a^{2} \cdot n^{2} \cdot π^{2} \cdot y = 0

Solve linear ODE:

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

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

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