Internal problem ID [2630]
Book: An introduction to the solution and applications of differential equations, J.W. Searl,
1966
Section: Chapter 4, Ex. 4.1
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, _dAlembert]
Solve \begin {gather*} \boxed {\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 33
dsolve([(x/(x^2+y(x)^2)+y(x)/x^2)+(y(x)/(x^2+y(x)^2)-1/x)*diff(y(x),x)=0,y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (\RootOf \left (4+4 \ln \relax (x )^{2}+4 \ln \relax (x ) \textit {\_Z} +\textit {\_Z}^{2}-4 \,{\mathrm e}^{\textit {\_Z}}\right )+2 \ln \relax (x )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.162 (sec). Leaf size: 28
DSolve[{(x/(x^2+y[x]^2)+y[x]/x^2)+(y[x]/(x^2+y[x]^2)-1/x)*y'[x]==0,y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)}{x}-\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=\log (x),y(x)\right ] \]