60.1.271 problem 272

Internal problem ID [10285]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 272
Date solved : Monday, January 27, 2025 at 06:50:20 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.116 (sec). Leaf size: 42

dsolve((y(x)^2+x^2)*diff(y(x),x)-y(x)^2=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {2 \sqrt {3}\, \operatorname {RootOf}\left (-2 \sqrt {3}\, {\mathrm e}^{\frac {2 \sqrt {3}\, \textit {\_Z}}{3}-c_{1}}+\sqrt {3}\, x -3 x \tan \left (\textit {\_Z} \right )\right )}{3}-c_{1}} \]

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 46

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]^2+1}{K[1] \left (K[1]^2-K[1]+1\right )}dK[1]=-\log (x)+c_1,y(x)\right ] \]