29.22.10 problem 616

Internal problem ID [5210]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 616
Date solved : Monday, January 27, 2025 at 10:21:06 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (x^{2}+2 y x -y^{2}\right ) y^{\prime }+x^{2}-2 y x +y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y \left (x \right ) = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2}-2 \textit {\_a} -1}{\textit {\_a}^{3}-3 \textit {\_a}^{2}+\textit {\_a} -1}d \textit {\_a} +\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.136 (sec). Leaf size: 91

DSolve[(x^2+2 x y[x]-y[x]^2)D[y[x],x]+x^2-2 x y[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3-3 \text {$\#$1}^2+\text {$\#$1}-1\&,\frac {\text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-2 \text {$\#$1} \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2-6 \text {$\#$1}+1}\&\right ]=-\log (x)+c_1,y(x)\right ] \]