Internal problem ID [6330]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime } y-y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.985 (sec). Leaf size: 53
dsolve(y(x)*diff(y(x),x)-y(x)=x,y(x), singsol=all)
\[ -\frac {\ln \left (-\frac {x^{2}+x y \relax (x )-y \relax (x )^{2}}{x^{2}}\right )}{2}-\frac {\sqrt {5}\, \arctanh \left (\frac {\left (x -2 y \relax (x )\right ) \sqrt {5}}{5 x}\right )}{5}-\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 63
DSolve[y[x]*y'[x] - y[x] == x,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{10} \left (\left (5+\sqrt {5}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {5}+1\right )-\left (\sqrt {5}-5\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {5}-1\right )\right )=-\log (x)+c_1,y(x)\right ] \]