73.6.14 problem 7.5 (d)

Internal problem ID [15153]
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)
Date solved : Tuesday, January 28, 2025 at 07:38:27 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} 1+\left (1-x \tan \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 108

dsolve(1+(1-x*tan(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \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 &= \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: 29

DSolve[1+(1-x*Tan[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=\sec (y(x)) \int _1^{y(x)}-\cos (K[1])dK[1]+c_1 \sec (y(x)),y(x)\right ] \]