Internal problem ID [3358]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 616.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (-y^{2}+2 y x +x^{2}\right ) y^{\prime }+x^{2}-2 y x +y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve((x^2+2*x*y(x)-y(x)^2)*diff(y(x),x)+x^2-2*x*y(x)+y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2}-2 \textit {\_a} -1}{\textit {\_a}^{3}-3 \textit {\_a}^{2}+\textit {\_a} -1}d \textit {\_a} +\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.119 (sec). Leaf size: 91
DSolve[(x^2+2 x y[x]-y[x]^2)y'[x]+x^2-2 x y[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3-3 \text {$\#$1}^2+\text {$\#$1}-1\&,\frac {\text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-2 \text {$\#$1} \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2-6 \text {$\#$1}+1}\&\right ]=-\log (x)+c_1,y(x)\right ] \]