Internal problem ID [7957]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 377.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+\left (x -2\right ) y^{\prime }-y+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.235 (sec). Leaf size: 25
dsolve(diff(y(x),x)^2+(x-2)*diff(y(x),x)-y(x)+1 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {1}{4} x^{2}+x \\ y \relax (x ) = c_{1}^{2}+c_{1} x -2 c_{1}+1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 27
DSolve[1 - y[x] + (-2 + x)*y'[x] + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+c_1 (x-2+c_1) \\ y(x)\to -\frac {1}{4} (x-4) x \\ \end{align*}