Internal problem ID [7677]
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]
Solve \begin {gather*} \boxed {x y^{\prime }-y^{2}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 11
dsolve(x*diff(y(x),x) - y(x)^2 + 1=0,y(x), singsol=all)
\[ y \relax (x ) = -\tanh \left (\ln \relax (x )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.511 (sec). Leaf size: 33
DSolve[x*y'[x] - y[x]^2 + 1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+\frac {2}{1+e^{2 c_1} x^2} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}