Internal problem ID [8761]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 425.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]
\[ \boxed {\left (1+x \right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 45
dsolve((x+1)*diff(y(x),x)^2-(x+y(x))*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= x +2-2 \sqrt {x +1} \\ y \left (x \right ) &= x +2+2 \sqrt {x +1} \\ y \left (x \right ) &= \frac {c_{1} \left (c_{1} x +c_{1} -x \right )}{c_{1} -1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 51
DSolve[y[x] - (x + y[x])*y'[x] + (1 + x)*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+\frac {c_1}{-1+c_1}\right ) \\ y(x)\to x-2 \sqrt {x+1}+2 \\ y(x)\to x+2 \sqrt {x+1}+2 \\ \end{align*}