Internal problem ID [5425]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page
15
Problem number: 4(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]
\[ \boxed {y^{\prime } x +2-x^{3} \left (y-1\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(x*diff(y(x),x)+2=x^3*(y(x)-1)*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (c_{1} {\mathrm e}^{\frac {1}{x^{2}}}\right ) x^{2}-1}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.366 (sec). Leaf size: 33
DSolve[x*y'[x]+2==x^3*(y[x]-1)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x^2}-W\left (e^{\frac {1}{x^2}+\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )}\right ) \\ \end{align*}