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

Internal problem ID [5783]
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
Date solved : Monday, January 27, 2025 at 01:17:45 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.079 (sec). Leaf size: 22

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

\begin{align*} y \left (x \right ) &= \arccos \left (\ln \left (x \right )+1\right ) x \\ y \left (x \right ) &= -\arccos \left (\ln \left (x \right )+1\right ) x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.456 (sec). Leaf size: 24

DSolve[{D[y[x],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*}