5.21 problem 18

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]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}-\sec \left (\frac {y}{x}\right )=0} \end {gather*}

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)
 

\[ y \relax (x ) = \arcsin \left (\ln \relax (x )+c_{1}\right ) x \]

Solution by Mathematica

Time used: 0.425 (sec). Leaf size: 13

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

\begin{align*} y(x)\to x \text {ArcSin}(\log (x)+c_1) \\ \end{align*}