29.20.25 problem 572

Internal problem ID [5166]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 572
Date solved : Monday, January 27, 2025 at 10:16:48 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 35

dsolve(x^2*(1-y(x))*diff(y(x),x)+(1+x)*y(x)^2 = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 5.181 (sec). Leaf size: 30

DSolve[x^2(1-y[x])D[y[x],x]+(1+x)y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{W\left (-\frac {e^{\frac {1}{x}-c_1}}{x}\right )} \\ y(x)\to 0 \\ \end{align*}