What is the solution for y^{''}+50y=0 ?

The solution for y^{''}+50y=0 is y=c_{1}cos(sqrt(2)*5t)+c_{2}sin(sqrt(2)*5t)

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y^{''}+50y=0

y^{^{''}} + 50 y = 0

y = c_{1} cos (2 \cdot 5 t) + c_{2} sin (2 \cdot 5 t)

Solution steps

y^{''} (t) + 50 y = 0

Solve linear ODE:

y = c_{1} cos (2 \cdot 5 t) + c_{2} sin (2 \cdot 5 t)

y = c_{1} cos (2 \cdot 5 t) + c_{2} sin (2 \cdot 5 t)

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

2 x^{^{''}} + 8 x^{^{'}} + 52 x = 0

y^{^{'''}} + 4 y^{^{''}} - 7 y^{^{'}} - 10 y = 0

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} - 20 y = 0, y (0) = 9, y (1) = 2

What is the solution for y^{''}+50y=0 ?
The solution for y^{''}+50y=0 is y=c_{1}cos(sqrt(2)*5t)+c_{2}sin(sqrt(2)*5t)