What is the solution for (dy)/(dx)=y*tan(x)+1 ?

The solution for (dy)/(dx)=y*tan(x)+1 is y=(sin(x))/(cos(x))+(c_{1})/(cos(x))

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(dy)/(dx)=y*tan(x)+1

\frac{d y}{d x} = y \cdot tan (x) + 1

y = \frac{sin ( x )}{cos ( x )} + \frac{c _{1}}{cos ( x )}

Solution steps

\frac{d y}{d x} = y \cdot tan (x) + 1

Solve linear ODE:

y = \frac{sin ( x )}{cos ( x )} + \frac{c _{1}}{cos ( x )}

y = \frac{sin ( x )}{cos ( x )} + \frac{c _{1}}{cos ( x )}

\frac{d ^{2}}{d x ^{2}} (2^{x^{2} + 1})

\frac{d y}{d x} = e^{5 y}

\frac{d}{d x} (e^{- 2 x} sin (x))

x \to - 1 lim (\frac{∣ x ∣}{x})

\frac{d P}{d t} = P (\frac{1}{t} - P)

What is the solution for (dy)/(dx)=y*tan(x)+1 ?
The solution for (dy)/(dx)=y*tan(x)+1 is y=(sin(x))/(cos(x))+(c_{1})/(cos(x))