What is the solution for y^{''}+16y=24sin(4t) ?

The solution for y^{''}+16y=24sin(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)-3tcos(4t)

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y^{''}+16y=24sin(4t)

y^{^{''}} + 16 y = 24 sin (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) - 3 t cos (4 t)

Solution steps

y^{''} (t) + 16 y = 24 sin (4 t)

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) - 3 t cos (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) - 3 t cos (4 t)

\int (\frac{x ^{2}}{x + 1}) d x

f (x) = - 3 x

\int (sin (x) - cos (x))^{2} d x

x^{3} - 27 x

x^{2} y^{^{'}} - y x = 0

What is the solution for y^{''}+16y=24sin(4t) ?
The solution for y^{''}+16y=24sin(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)-3tcos(4t)