Internal problem ID [995]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime }-\frac {y}{x}-\sec \left (\frac {y}{x}\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve(diff(y(x),x)=y(x)/x+sec(y(x)/x),y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.409 (sec). Leaf size: 13
DSolve[y'[x]==y[x]/x+Sec[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \arcsin (\log (x)+c_1) \]