64.7.7 problem 7

Internal problem ID [13381]
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 : Tuesday, January 28, 2025 at 05:36:15 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*}

✓ Solution by Maple

Time used: 1.430 (sec). Leaf size: 32

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

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

✓ Solution by Mathematica

Time used: 0.160 (sec). Leaf size: 53

DSolve[(5*x+2*y[x]+1)+(2*x+y[x]+1)*D[y[x],x]==0,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*}