Internal problem ID [13247]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 2. Integration and differential equations. Additional exercises. page
32
Problem number: 2.2 (e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime }=2 x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(y(x)*diff(y(x),x)=2*x,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {2 x^{2}+c_{1}} \\ y \left (x \right ) &= -\sqrt {2 x^{2}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 42
DSolve[y[x]*y'[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt {x^2+c_1} \\ y(x)\to \sqrt {2} \sqrt {x^2+c_1} \\ \end{align*}