What is the solution for (dx)/(dt)-(tan(t))x=sin(t),x(0)=1 ?

The solution for (dx)/(dt)-(tan(t))x=sin(t),x(0)=1 is x=(sin^2(t))/(2cos(t))+1/(cos(t))

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(dx)/(dt)-(tan(t))x=sin(t),x(0)=1

\frac{d x}{d t} - (tan (t)) x = sin (t), x (0) = 1

x = \frac{sin ^{2} ( t )}{2 cos ( t )} + \frac{1}{cos ( t )}

Solution steps

\frac{d x}{d t} - (tan (t)) x = sin (t)

Solve linear ODE:

x = \frac{sin ^{2} ( t )}{2 cos ( t )} + \frac{1}{cos ( t )}

x = \frac{sin ^{2} ( t )}{2 cos ( t )} + \frac{1}{cos ( t )}

What is the solution for (dx)/(dt)-(tan(t))x=sin(t),x(0)=1 ?
The solution for (dx)/(dt)-(tan(t))x=sin(t),x(0)=1 is x=(sin^2(t))/(2cos(t))+1/(cos(t))