Internal problem ID [80]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {2 x y y^{\prime }-y^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(2*x*y(x)*diff(y(x),x) = x^2+y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {c_{1} x +x^{2}} y \left (x \right ) = -\sqrt {c_{1} x +x^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.17 (sec). Leaf size: 38
DSolve[2*x*y[x]*y'[x] == x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {x+c_1} y(x)\to \sqrt {x} \sqrt {x+c_1} \end{align*}