Internal problem ID [3821]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 571.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 33
dsolve(x^2*(1-y(x))*diff(y(x),x)+(1-x)*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = x \,{\mathrm e}^{\frac {-\operatorname {LambertW}\left (-x \,{\mathrm e}^{\frac {c_{1} x +1}{x}}\right ) x +c_{1} x +1}{x}} \]
✓ Solution by Mathematica
Time used: 4.497 (sec). Leaf size: 26
DSolve[x^2(1-y[x])y'[x]+(1-x)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -W\left (x \left (-e^{\frac {1}{x}-c_1}\right )\right ) \\ y(x)\to 0 \\ \end{align*}