12.1.18 problem 10(a)

Internal problem ID [1536]
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)
Date solved : Monday, January 27, 2025 at 04:59:12 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y^{\prime }&=-\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \end{align*}

✓ 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)
 

\[ x -\sqrt {x^{2}+4 x +4 y}-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.841 (sec). Leaf size: 47

DSolve[D[y[x],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*}