What is the solution for (dy)/(dt)+y=cos(2t),y(0)=5 ?

The solution for (dy)/(dt)+y=cos(2t),y(0)=5 is y=(2sin(2t))/5+(cos(2t))/5+(24)/(5e^t)

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(dy)/(dt)+y=cos(2t),y(0)=5

\frac{d y}{d t} + y = cos (2 t), y (0) = 5

y = \frac{2 sin ( 2 t )}{5} + \frac{cos ( 2 t )}{5} + \frac{24}{5 e ^{t}}

Solution steps

\frac{d y}{d t} + y = cos (2 t)

Solve linear ODE:

y = \frac{2 sin ( 2 t )}{5} + \frac{cos ( 2 t )}{5} + \frac{24}{5 e ^{t}}

y = \frac{2 sin ( 2 t )}{5} + \frac{cos ( 2 t )}{5} + \frac{24}{5 e ^{t}}

\frac{d y}{d x} = \frac{1}{x y}

f (x) = x x^{3} - 6

y = 2 x^{2} 2 - x

\frac{\partial}{\partial x} (e^{- 1} cos (π x))

\frac{d x}{d t} = \frac{2 x}{t}, x (3) = 1

What is the solution for (dy)/(dt)+y=cos(2t),y(0)=5 ?
The solution for (dy)/(dt)+y=cos(2t),y(0)=5 is y=(2sin(2t))/5+(cos(2t))/5+(24)/(5e^t)