73.5.21 problem 6.7 (i)

Internal problem ID [15061]
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)
Date solved : Monday, March 31, 2025 at 01:20:32 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 19

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

\[ x -\sqrt {2 x +y-3}-c_1 = 0 \]

✓ Mathematica. Time used: 0.696 (sec). Leaf size: 34

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

\begin{align*} y(x)\to x^2+2 e^{c_1} (x+1)+4+e^{2 c_1} \\ y(x)\to x^2+4 \\ \end{align*}

✓ Sympy. Time used: 0.731 (sec). Leaf size: 12

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

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