Internal problem ID [13417]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.5 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\left (1-\tan \left (y\right ) x \right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 108
dsolve(1+(1-x*tan(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \arctan \left (\frac {-\sqrt {-c_{1}^{2}+x^{2}+1}\, x +c_{1}}{x^{2}+1}, \frac {c_{1} x +\sqrt {-c_{1}^{2}+x^{2}+1}}{x^{2}+1}\right ) \\ y \left (x \right ) &= \arctan \left (\frac {\sqrt {-c_{1}^{2}+x^{2}+1}\, x +c_{1}}{x^{2}+1}, \frac {c_{1} x -\sqrt {-c_{1}^{2}+x^{2}+1}}{x^{2}+1}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 145
DSolve[1+(1-x*Tan[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}\left (\frac {c_1 x-\sqrt {x^2+1-c_1{}^2}}{-1+c_1{}^2}\right ) \\ y(x)\to \sec ^{-1}\left (\frac {c_1 x-\sqrt {x^2+1-c_1{}^2}}{-1+c_1{}^2}\right ) \\ y(x)\to -\sec ^{-1}\left (\frac {\sqrt {x^2+1-c_1{}^2}+c_1 x}{-1+c_1{}^2}\right ) \\ y(x)\to \sec ^{-1}\left (\frac {\sqrt {x^2+1-c_1{}^2}+c_1 x}{-1+c_1{}^2}\right ) \\ \end{align*}