64.7.11 problem 11

Internal problem ID [13306]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page 67
Problem number : 11
Date solved : Wednesday, March 05, 2025 at 09:42:37 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.668 (sec). Leaf size: 23

ode:=6*x+4*y(x)+1+(4*x+2*y(x)+2)*diff(y(x),x) = 0; 
ic:=y(1/2) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -2 x -1+\frac {\sqrt {4 x^{2}+12 x +93}}{2} \]

✓ Mathematica. Time used: 0.151 (sec). Leaf size: 28

ode=(6*x+4*y[x]+1)+(4*x+2*y[x]+2)*D[y[x],x]==0; 
ic={y[1/2]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} \left (\sqrt {4 x^2+12 x+93}-4 x-2\right ) \]

✓ Sympy. Time used: 2.208 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x + (4*x + 2*y(x) + 2)*Derivative(y(x), x) + 4*y(x) + 1,0) 
ics = {y(1/2): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 2 x + \frac {\sqrt {4 x^{2} + 12 x + 93}}{2} - 1 \]