Internal problem ID [3928]
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 7.11, page
61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {{\mathrm e}^{\frac {y}{x}} x -y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 63
dsolve((x*exp(y(x)/x)-y(x)*sin(y(x)/x))+x*sin(y(x)/x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left ({\mathrm e}^{2 \textit {\_Z}} \left (4 \ln \relax (x )^{2} {\mathrm e}^{2 \textit {\_Z}}+8 \ln \relax (x ) {\mathrm e}^{2 \textit {\_Z}} c_{1}+4 c_{1}^{2} {\mathrm e}^{2 \textit {\_Z}}-4 \sin \left (\textit {\_Z} \right ) \ln \relax (x ) {\mathrm e}^{\textit {\_Z}}-4 \sin \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z}} c_{1}+2 \left (\sin ^{2}\left (\textit {\_Z} \right )\right )-1\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.327 (sec). Leaf size: 39
DSolve[(x*Exp[y[x]/x]-y[x]*Sin[y[x]/x])+x*Sin[y[x]/x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{2} e^{-\frac {y(x)}{x}} \left (\sin \left (\frac {y(x)}{x}\right )+\cos \left (\frac {y(x)}{x}\right )\right )=-\log (x)+c_1,y(x)\right ] \]