Internal problem ID [3001]
Book: Applied Differential equations, N Curle, 1971
Section: Examples, page 35
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, _Riccati]
\[ \boxed {y^{\prime } x^{2}-x \left (y-1\right )-\left (y-1\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.203 (sec). Leaf size: 23
DSolve[x^2*y'[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*}