58.7.7 problem 7

Internal problem ID [14662]
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 : 7
Date solved : Thursday, October 02, 2025 at 09:49:02 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.126 (sec). Leaf size: 32

ode:=5*x+2*y(x)+1+(2*x+y(x)+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {-\left (x -1\right )^{2} c_1^{2}+1}+\left (-2 x -1\right ) c_1}{c_1} \]

✓ Mathematica. Time used: 0.093 (sec). Leaf size: 53

ode=(5*x+2*y[x]+1)+(2*x+y[x]+1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {-x^2+2 x+1+c_1}-2 x-1\\ y(x)&\to \sqrt {-x^2+2 x+1+c_1}-2 x-1 \end{align*}

✓ Sympy. Time used: 1.258 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*x + (2*x + y(x) + 1)*Derivative(y(x), x) + 2*y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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