50.3.23 problem 4(c)

Internal problem ID [7847]
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)
Date solved : Monday, January 27, 2025 at 03:25:39 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

\begin{align*} x y^{\prime }+2&=x^{3} \left (y-1\right ) y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 22

dsolve(x*diff(y(x),x)+2=x^3*(y(x)-1)*diff(y(x),x),y(x), singsol=all)
 

\[ y = \frac {-\operatorname {LambertW}\left (c_{1} {\mathrm e}^{\frac {1}{x^{2}}}\right ) x^{2}+1}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.336 (sec). Leaf size: 33

DSolve[x*D[y[x],x]+2==x^3*(y[x]-1)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{x^2}-W\left (e^{\frac {1}{x^2}+\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )}\right ) \]