Internal problem ID [3930]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number: First order with homogeneous Coefficients. Exercise 7.14, page
61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 16
dsolve([diff(y(x),x)-y(x)/x+csc(y(x)/x)=0,y(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = x \left (1-2 \_B21 \right ) \arccos \left (\ln \left (x \right )+1\right ) \]
✓ Solution by Mathematica
Time used: 0.399 (sec). Leaf size: 24
DSolve[{y'[x]-y[x]/x+Csc[y[x]/x]==0,y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \arccos (\log (x)+1) \\ y(x)\to x \arccos (\log (x)+1) \\ \end{align*}