67.5.22 problem 6.7 (j)

Internal problem ID [16420]
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 : Thursday, October 02, 2025 at 01:31:13 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 57

ode:=diff(y(x),x) = 2*(2*x+y(x)-3)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ x -\sqrt {2 x +y-3}-\frac {\ln \left (-1+\sqrt {2 x +y-3}\right )}{2}+\frac {\ln \left (\sqrt {2 x +y-3}+1\right )}{2}+\frac {\ln \left (-4+y+2 x \right )}{2}-c_1 = 0 \]

✓ Mathematica. Time used: 5.397 (sec). Leaf size: 51

ode=D[y[x],x]==2*Sqrt[2*x+y[x]-3]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.649 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*sqrt(2*x + y(x) - 3) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 2 x + \left (W\left (C_{1} e^{- x - 1}\right ) + 1\right )^{2} + 3 \]