78.6.16 problem 4 (c)

Internal problem ID [18184]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 10 (Linear equations). Problems at page 82
Problem number : 4 (c)
Date solved : Tuesday, January 28, 2025 at 11:37:26 AM
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: 0.007 (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: 0.063 (sec). Leaf size: 18

DSolve[y[x]-x*D[y[x],x]==D[y[x],x]*y[x]^2*Exp[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=e^{y(x)} y(x)+c_1 y(x),y(x)\right ] \]