29.20.24 problem 571

Internal problem ID [5165]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 571
Date solved : Monday, January 27, 2025 at 10:16:46 AM
CAS classification : [_separable]

\begin{align*} x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (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: 4.002 (sec). Leaf size: 26

DSolve[x^2(1-y[x])D[y[x],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*}