Internal problem ID [2015]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } y x +y^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(x*y(x)*diff(y(x),x)=(x^2-y(x)^2),y(x), singsol=all)
\begin{align*} y = -\frac {\sqrt {2 x^{4}+4 c_{1}}}{2 x} y = \frac {\sqrt {2 x^{4}+4 c_{1}}}{2 x} \end{align*}
✓ Solution by Mathematica
Time used: 0.21 (sec). Leaf size: 46
DSolve[x*y[x]*y'[x]==(x^2-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\frac {x^4}{2}+c_1}}{x} y(x)\to \frac {\sqrt {\frac {x^4}{2}+c_1}}{x} \end{align*}