Internal problem ID [8713]
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]
\[ \boxed {{y^{\prime }}^{2}+\left (x -2\right ) y^{\prime }-y=-1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
dsolve(diff(y(x),x)^2+(x-2)*diff(y(x),x)-y(x)+1 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {1}{4} x^{2}+x \\ y \left (x \right ) &= 1+c_{1}^{2}+\left (x -2\right ) c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 29
DSolve[1 - y[x] + (-2 + x)*y'[x] + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x-2)+1+c_1{}^2 \\ y(x)\to -\frac {1}{4} (x-4) x \\ \end{align*}