What is the solution for y^{''}+y=6sin(2t)+4tcos(2t) ?

The solution for y^{''}+y=6sin(2t)+4tcos(2t) is y=c_{1}cos(t)+c_{2}sin(t)-(4tcos(2t))/3-2/9 sin(2t)

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y^{''}+y=6sin(2t)+4tcos(2t)

y^{^{''}} + y = 6 sin (2 t) + 4 t cos (2 t)

y = c_{1} cos (t) + c_{2} sin (t) - \frac{4 t cos ( 2 t )}{3} - \frac{2}{9} sin (2 t)

Solution steps

y^{''} (t) + y = 6 sin (2 t) + 4 t cos (2 t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) - \frac{4 t cos ( 2 t )}{3} - \frac{2}{9} sin (2 t)

y = c_{1} cos (t) + c_{2} sin (t) - \frac{4 t cos ( 2 t )}{3} - \frac{2}{9} sin (2 t)

\frac{d}{d x} (600000 (0.8)^{x})

y = \frac{4}{ln ( x )}

\int \frac{x ^{4} + 1}{x ^{5} + 4 x ^{3}} d x

n = 1 \sum \infty (- 1)^{n - 1}

\frac{\partial}{\partial x} (2 x y - x^{3} - y^{2})

What is the solution for y^{''}+y=6sin(2t)+4tcos(2t) ?
The solution for y^{''}+y=6sin(2t)+4tcos(2t) is y=c_{1}cos(t)+c_{2}sin(t)-(4tcos(2t))/3-2/9 sin(2t)