22.1.4 problem 4

Internal problem ID [4090]
Book : Applied Differential equations, Newby Curle. Van Nostrand Reinhold. 1972
Section : Examples, page 35
Problem number : 4
Date solved : Monday, January 27, 2025 at 08:08:20 AM
CAS classification : [[_homogeneous, `class C`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 15

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

\[ y \left (x \right ) = 1-\frac {x}{\ln \left (x \right )+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 23

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

\begin{align*} y(x)\to 1+\frac {x}{-\log (x)+c_1} \\ y(x)\to 1 \\ \end{align*}