Internal problem ID [3014]
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]
\[ \boxed {y^{\prime }-\frac {y^{2}+x^{2}}{2 x^{2}}=0} \]
✓ 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)
\[ y \left (x \right ) = \frac {x \left (\ln \left (x \right )+c_{1} -2\right )}{\ln \left (x \right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.149 (sec). Leaf size: 29
DSolve[y'[x]==(x^2+y[x]^2)/(2*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (\log (x)-2+2 c_1)}{\log (x)+2 c_1} y(x)\to x \end{align*}