What is the solution for (dy)/(dt)+tan(t)y=3sin(t),y(0)=1 ?

The solution for (dy)/(dt)+tan(t)y=3sin(t),y(0)=1 is y=-(3ln(cos(t)))/(sec(t))+1/(sec(t))

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(dy)/(dt)+tan(t)y=3sin(t),y(0)=1

\frac{d y}{d t} + tan (t) y = 3 sin (t), y (0) = 1

y = - \frac{3 ln ( cos ( t ) )}{sec ( t )} + \frac{1}{sec ( t )}

Solution steps

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

Solve linear ODE:

y = - \frac{3 ln ( cos ( t ) )}{sec ( t )} + \frac{1}{sec ( t )}

y = - \frac{3 ln ( cos ( t ) )}{sec ( t )} + \frac{1}{sec ( t )}

\frac{d y}{d x} = \frac{3 x ^{2}}{y ( 1 - x ^{3} )}

\frac{d}{d x} (- 32 cos (8 x))

\frac{d}{d x} (\frac{2 x + 9}{2 x})

f (x) = x^{2} + x - 2

\frac{d}{d x} (\frac{cos ( x )}{ln ( x )})

What is the solution for (dy)/(dt)+tan(t)y=3sin(t),y(0)=1 ?
The solution for (dy)/(dt)+tan(t)y=3sin(t),y(0)=1 is y=-(3ln(cos(t)))/(sec(t))+1/(sec(t))