Internal problem ID [13076]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.7 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-2 \sqrt {2 x +y-3}=-2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x)=2*sqrt(2*x+y(x)-3)-2,y(x), singsol=all)
\[ x -\sqrt {2 x +y-3}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.256 (sec). Leaf size: 38
DSolve[y'[x]==2*Sqrt[2*x+y[x]-3]-2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2-e^{c_1} (x+1)+4+\frac {e^{2 c_1}}{4} y(x)\to x^2+4 \end{align*}