73.5.22 problem 6.7 (j)

Internal problem ID [15133]
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)
Date solved : Tuesday, January 28, 2025 at 07:36:09 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=2 \sqrt {2 x +y-3} \end{align*}

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 57

dsolve(diff(y(x),x)=2*sqrt(2*x+y(x)-3),y(x), singsol=all)
 

\[ x -\sqrt {2 x +y-3}-\frac {\ln \left (-1+\sqrt {2 x +y-3}\right )}{2}+\frac {\ln \left (\sqrt {2 x +y-3}+1\right )}{2}+\frac {\ln \left (2 x +y-4\right )}{2}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 7.911 (sec). Leaf size: 51

DSolve[D[y[x],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*}