Internal problem ID [2505]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}+y^{2}}{2 x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x)=(x^2+y(x)^2)/(2*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (\ln \relax (x )+c_{1}-2\right )}{\ln \relax (x )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 24
DSolve[y'[x]==(x^2+y[x]^2)/(2*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\frac {2 x}{\log (x)+2 c_1} \\ y(x)\to x \\ \end{align*}