Internal problem ID [8433]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 96.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } x -y^{2}=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(x*diff(y(x),x) - y(x)^2 + 1=0,y(x), singsol=all)
\[ y \left (x \right ) = -\tanh \left (\ln \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.492 (sec). Leaf size: 43
DSolve[x*y'[x] - y[x]^2 + 1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1-e^{2 c_1} x^2}{1+e^{2 c_1} x^2} y(x)\to -1 y(x)\to 1 \end{align*}