What is the solution for (dy)/(dt)+3y=13sin(2t),y(0)=6 ?

The solution for (dy)/(dt)+3y=13sin(2t),y(0)=6 is y=-2cos(2t)+3sin(2t)+8/(e^{3t)}

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(dy)/(dt)+3y=13sin(2t),y(0)=6

\frac{d y}{d t} + 3 y = 13 sin (2 t), y (0) = 6

y = - 2 cos (2 t) + 3 sin (2 t) + \frac{8}{e ^{3 t}}

Solution steps

\frac{d y}{d t} + 3 y = 13 sin (2 t)

Solve linear ODE:

y = - 2 cos (2 t) + 3 sin (2 t) + \frac{8}{e ^{3 t}}

y = - 2 cos (2 t) + 3 sin (2 t) + \frac{8}{e ^{3 t}}

f (x) = x^{4} + 7 x^{2} - x, (1, 7)

\int_{0}^{3} (x^{3} - x) d x

x \frac{d}{d x} (ln (y)) = 1

x \to 2 + lim (\frac{1}{x + 2})

\frac{d}{d x} (33 (10 x - x + 10.45))

What is the solution for (dy)/(dt)+3y=13sin(2t),y(0)=6 ?
The solution for (dy)/(dt)+3y=13sin(2t),y(0)=6 is y=-2cos(2t)+3sin(2t)+8/(e^{3t)}