Internal problem ID [3909]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 12.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {y-y^{\prime } x -y^{\prime }+\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.218 (sec). Leaf size: 27
dsolve(y(x)=x*diff(y(x),x)+diff(y(x),x)-(diff(y(x),x))^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{4} x^{2}+\frac {1}{2} x +\frac {1}{4} \\ y \relax (x ) = c_{1} x -c_{1}^{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 28
DSolve[y[x]==x*y'[x]+y'[x]-(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x+1-c_1) \\ y(x)\to \frac {1}{4} (x+1)^2 \\ \end{align*}