Internal problem ID [577]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {y y^{\prime }}{y-2}=-\frac {-x^{2}+x +1}{x^{2}}} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 26
dsolve((-x^2+x+1)/x^2+y(x)*diff(y(x),x)/(-2+y(x)) = 0,y(x), singsol=all)
\[ y \left (x \right ) = 2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{\frac {x}{2}-1+\frac {1}{2 x}}}{2 \sqrt {x}}\right )+2 \]
✓ Solution by Mathematica
Time used: 60.036 (sec). Leaf size: 63
DSolve[(-x^2+x+1)/x^2+y[x]*y'[x]/(-2+y[x]) == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \left (1+W\left (-\frac {1}{2} \sqrt {\frac {e^{x+\frac {1}{x}-2+c_1}}{x}}\right )\right ) y(x)\to 2 \left (1+W\left (\frac {1}{2} \sqrt {\frac {e^{x+\frac {1}{x}-2+c_1}}{x}}\right )\right ) \end{align*}