What is the solution for y^{''}+1960y=0 ?

The solution for y^{''}+1960y=0 is y=c_{1}cos(14sqrt(10)t)+c_{2}sin(14sqrt(10)t)

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y^{''}+1960y=0

y^{^{''}} + 1960 y = 0

y = c_{1} cos (1410 t) + c_{2} sin (1410 t)

Solution steps

y^{''} (t) + 1960 y = 0

Solve linear ODE:

y = c_{1} cos (1410 t) + c_{2} sin (1410 t)

y = c_{1} cos (1410 t) + c_{2} sin (1410 t)

y^{^{''}} + 9 y^{^{'}} + 0 y = 0

y^{^{'''}} + 9 y^{^{''}} + 24 y^{^{'}} + 16 y = 0

2 x^{^{''}} + 16 x^{^{'}} + 64 x = 0, x (0) = 0, x^{^{'}} (0) = 0.2

y^{^{''}} + 10 y^{^{'}} + 8 y = 0

y^{^{'''}} + 8 y^{^{''}} + 19 y^{^{'}} + 12 y = 0

What is the solution for y^{''}+1960y=0 ?
The solution for y^{''}+1960y=0 is y=c_{1}cos(14sqrt(10)t)+c_{2}sin(14sqrt(10)t)