Internal problem ID [1965]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\frac {2 x^{2}}{x^{2}+y^{2}}+\ln \left (x^{2}+y^{2}\right )+\frac {2 x y y^{\prime }}{x^{2}+y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 39
dsolve((2*x^2/(x^2+y(x)^2)+ln(x^2+y(x)^2))+(2*x*y(x))/(x^2+y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {-x^{2}+{\mathrm e}^{-\frac {c_{1}}{x}}} \\ y \left (x \right ) &= -\sqrt {-x^{2}+{\mathrm e}^{-\frac {c_{1}}{x}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.823 (sec). Leaf size: 47
DSolve[(2*x^2/(x^2+y[x]^2)+Log[x^2+y[x]^2])+(2*x*y[x])/(x^2+y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2+e^{\frac {c_1}{x}}} \\ y(x)\to \sqrt {-x^2+e^{\frac {c_1}{x}}} \\ \end{align*}