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]
\[ \boxed {y^{\prime }-\frac {\sqrt {x^{2}+4 x +4 y}}{2}=-\frac {x}{2}-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(y(x),x) = 1/2*(-(x+2)+sqrt(x^2+4*x+4*y(x))),y(x), singsol=all)
\[ x -\sqrt {x^{2}+4 x +4 y \left (x \right )}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.801 (sec). Leaf size: 47
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+2 e^{c_1} (x+1)+1+e^{2 c_1}\right ) \\ y(x)\to 1 \\ y(x)\to \frac {1}{4} (1-2 x) \\ \end{align*}