What is the solution for (dy)/(dt)+1/2 y=17sin(2t),y(0)=-1 ?

The solution for (dy)/(dt)+1/2 y=17sin(2t),y(0)=-1 is y=2(sin(2t)-4cos(2t))+7/(e^{t/2)}

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(dy)/(dt)+1/2 y=17sin(2t),y(0)=-1

\frac{d y}{d t} + \frac{1}{2} y = 17 sin (2 t), y (0) = - 1

y = 2 (sin (2 t) - 4 cos (2 t)) + \frac{7}{e ^{\frac{t}{2}}}

Solution steps

\frac{d y}{d t} + \frac{1}{2} y = 17 sin (2 t)

Solve linear ODE:

y = 2 (sin (2 t) - 4 cos (2 t)) + \frac{7}{e ^{\frac{t}{2}}}

y = 2 (sin (2 t) - 4 cos (2 t)) + \frac{7}{e ^{\frac{t}{2}}}

\int x^{- 2} + x^{\frac{1}{5}} d x

\frac{d}{d x} (arctan (s x))

\frac{d}{d x} (tan (x - y))

3 cos (8 t)

What is the solution for (dy)/(dt)+1/2 y=17sin(2t),y(0)=-1 ?
The solution for (dy)/(dt)+1/2 y=17sin(2t),y(0)=-1 is y=2(sin(2t)-4cos(2t))+7/(e^{t/2)}