73.5.1 problem 6.1 (a)

Internal problem ID [15033]
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 : 6.1 (a)
Date solved : Thursday, March 13, 2025 at 05:28:08 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {1}{\left (3 x +3 y+2\right )^{2}} \end{align*}

✓ Maple. Time used: 0.124 (sec). Leaf size: 24

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

\[ y = -c_{1} +\frac {\operatorname {RootOf}\left (-\textit {\_Z} +3 c_{1} -3 x -2+\tan \left (\textit {\_Z} \right )\right )}{3} \]

✓ Mathematica. Time used: 0.2 (sec). Leaf size: 135

ode=D[y[x],x]==1/(3*x+3*y[x]+2)^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (-\int _1^x\frac {18 K[1]+18 K[2]+12}{\left (9 K[1]^2+18 K[2] K[1]+12 K[1]+9 K[2]^2+12 K[2]+5\right )^2}dK[1]-\frac {1}{9 x^2+18 K[2] x+12 x+9 K[2]^2+12 K[2]+5}+1\right )dK[2]+\int _1^x-\frac {1}{9 K[1]^2+18 y(x) K[1]+12 K[1]+9 y(x)^2+12 y(x)+5}dK[1]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.028 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/(3*x + 3*y(x) + 2)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} - y{\left (x \right )} + \frac {\operatorname {atan}{\left (3 x + 3 y{\left (x \right )} + 2 \right )}}{3} = 0 \]