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

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

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

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

y = 2 (sin (2 t) - 4 cos (2 t)) + \frac{c _{1}}{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{c _{1}}{e ^{\frac{t}{2}}}

y = 2 (sin (2 t) - 4 cos (2 t)) + \frac{c _{1}}{e ^{\frac{t}{2}}}

\int cos (2 x) d x

\int (tan (x))^{4} d x

\frac{d}{d x} (\frac{x ^{2} - 5 x + 4}{∣ x - 1 ∣})

\frac{d}{d x} (x^{1 - a})

\frac{\partial}{\partial x} (e^{\frac{y}{x}} \cdot y)

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