What is the solution for y^{''}+49pi^2y=0 ?

The solution for y^{''}+49pi^2y=0 is y=c_{1}cos(7pit)+c_{2}sin(7pit)

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y^{''}+49pi^2y=0

y^{^{''}} + 49 π^{2} y = 0

y = c_{1} cos (7 π t) + c_{2} sin (7 π t)

Solution steps

y^{''} (t) + 49 π^{2} y = 0

Solve linear ODE:

y = c_{1} cos (7 π t) + c_{2} sin (7 π t)

y = c_{1} cos (7 π t) + c_{2} sin (7 π t)

\frac{d ^{2} x}{d t ^{2}} + 15 \frac{d x}{d t} + 56 x = 0

4 f (x) = f^{^{''}} (x)

y^{^{''}} + 6 y^{^{'}} = 0, y (0) = - 4, y^{^{'}} (0) = 6

y^{^{''}} = 7 y^{^{'}} - 10 y, y (0) = 0, y^{^{'}} (0) = - 3

\frac{1}{4} y^{^{''}} + 3 y^{^{'}} + 4 y = 0

What is the solution for y^{''}+49pi^2y=0 ?
The solution for y^{''}+49pi^2y=0 is y=c_{1}cos(7pit)+c_{2}sin(7pit)