Internal problem ID [1907]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 6, page 25
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2}-y^{\prime } x y=-x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve((x^2+y(x)^2)=x*y(x)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {2 \ln \left (x \right )+c_{1}}\, x \\ y \left (x \right ) &= -\sqrt {2 \ln \left (x \right )+c_{1}}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.17 (sec). Leaf size: 36
DSolve[(x^2+y[x]^2)==x*y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {2 \log (x)+c_1} \\ y(x)\to x \sqrt {2 \log (x)+c_1} \\ \end{align*}