What is the solution for y^{''}+y=7sin(2t)+5tcos(2t) ?

The solution for y^{''}+y=7sin(2t)+5tcos(2t) is y=c_{1}cos(t)+c_{2}sin(t)-(5tcos(2t))/3-1/9 sin(2t)

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y^{''}+y=7sin(2t)+5tcos(2t)

y^{^{''}} + y = 7 sin (2 t) + 5 t cos (2 t)

y = c_{1} cos (t) + c_{2} sin (t) - \frac{5 t cos ( 2 t )}{3} - \frac{1}{9} sin (2 t)

Solution steps

y^{''} (t) + y = 7 sin (2 t) + 5 t cos (2 t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) - \frac{5 t cos ( 2 t )}{3} - \frac{1}{9} sin (2 t)

y = c_{1} cos (t) + c_{2} sin (t) - \frac{5 t cos ( 2 t )}{3} - \frac{1}{9} sin (2 t)

\frac{24}{( 4 x - 17 ) ^{\frac{5}{2}}}

y = 8 9 x^{2} + 7

y = arccos (4 x)

x \to \infty lim (x + 1)

(e^{t} cos (t) + e^{t} sin (t) + e^{t})^{^{'}}

What is the solution for y^{''}+y=7sin(2t)+5tcos(2t) ?
The solution for y^{''}+y=7sin(2t)+5tcos(2t) is y=c_{1}cos(t)+c_{2}sin(t)-(5tcos(2t))/3-1/9 sin(2t)