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}}

x \to 3 + lim (\frac{x - 4}{3 - x})

d er i v a t i v e u

t an g e n t f (x) = x^{3} - 3 x + 1

n \to \infty lim (x^{2 n})

\frac{d}{d x} (\frac{x ^{2} - 16}{x - 4})

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)}