Internal problem ID [886]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 1, Introduction. Section 1.2 Page 14
Problem number: 10(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {y^{\prime }+1+\frac {x}{2}-\frac {\sqrt {x^{2}+4 x +4 y}}{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x) = 1/2*(-(x+2)+sqrt(x^2+4*x+4*y(x))),y(x), singsol=all)
\[ x -2 \sqrt {y \relax (x )+\frac {x^{2}}{4}+x}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.794 (sec). Leaf size: 46
DSolve[y'[x] ==1/2*(-(x+2)+Sqrt[x^2+4*x+4*y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-2 x+e^{c_1} \left (2 x+2+e^{c_1}\right )+1\right ) \\ y(x)\to 1 \\ y(x)\to \frac {1}{4} (1-2 x) \\ \end{align*}