1.13 problem First order with homogeneous Coefficients. Exercise 7.14, page 61

Internal problem ID [3931]

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]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}

Solution by Maple

Time used: 0.125 (sec). Leaf size: 16

dsolve([diff(y(x),x)-y(x)/x+csc(y(x)/x)=0,y(1) = 0],y(x), singsol=all)
 

\[ y \relax (x ) = \left (-2 \_B1 x +x \right ) \arccos \left (\ln \relax (x )+1\right ) \]

Solution by Mathematica

Time used: 0.405 (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 \text {ArcCos}(\log (x)+1) \\ y(x)\to x \text {ArcCos}(\log (x)+1) \\ \end{align*}