12.5.21 problem 18

Internal problem ID [1645]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 18
Date solved : Monday, January 27, 2025 at 05:15:49 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 11

dsolve(diff(y(x),x)=y(x)/x+sec(y(x)/x),y(x), singsol=all)
 

\[ y = \arcsin \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Solution by Mathematica

Time used: 0.363 (sec). Leaf size: 13

DSolve[D[y[x],x]==y[x]/x+Sec[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \arcsin (\log (x)+c_1) \]