47.2.6 problem 6

Internal problem ID [7422]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 6
Date solved : Monday, January 27, 2025 at 02:54:32 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 10

dsolve(x*diff(y(x),x)-y(x)=x*tan(y(x)/x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 9.413 (sec). Leaf size: 19

DSolve[x*D[y[x],x]-y[x]==x*Tan[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \arcsin \left (e^{c_1} x\right ) \\ y(x)\to 0 \\ \end{align*}