73.5.14 problem 6.7 (b)

Internal problem ID [15046]
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 (b)
Date solved : Thursday, March 13, 2025 at 05:31:51 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} 3 y^{\prime }&=-2+\sqrt {2 x +3 y+4} \end{align*}

✓ Maple. Time used: 0.075 (sec). Leaf size: 21

ode:=3*diff(y(x),x) = -2+(2*x+3*y(x)+4)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ x -2 \sqrt {2 x +3 y+4}-c_{1} = 0 \]

✓ Mathematica. Time used: 0.831 (sec). Leaf size: 48

ode=3*D[y[x],x]==-2+Sqrt[2*x+3*y[x]+4]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{12} \left (x^2-6 x+2 e^{c_1} (x+1)-15+e^{2 c_1}\right ) \\ y(x)\to \frac {1}{12} \left (x^2-6 x-15\right ) \\ \end{align*}

✓ Sympy. Time used: 0.792 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(2*x + 3*y(x) + 4) + 3*Derivative(y(x), x) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {2 x}{3} + \frac {\left (C_{1} + x\right )^{2}}{12} - \frac {4}{3} \]