Internal problem ID [13077]
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 (j).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-2 \sqrt {2 x +y-3}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 57
dsolve(diff(y(x),x)=2*sqrt(2*x+y(x)-3),y(x), singsol=all)
\[ x -\sqrt {2 x +y-3}-\frac {\ln \left (\sqrt {2 x +y-3}-1\right )}{2}+\frac {\ln \left (\sqrt {2 x +y-3}+1\right )}{2}+\frac {\ln \left (-4+2 x +y\right )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 8.176 (sec). Leaf size: 51
DSolve[y'[x]==2*Sqrt[2*x+y[x]-3],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to W\left (-e^{-x+\frac {1}{2}+c_1}\right ){}^2+2 W\left (-e^{-x+\frac {1}{2}+c_1}\right )-2 x+4 y(x)\to 4-2 x \end{align*}