Internal problem ID [11705]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y+\left (2 x +y+1\right ) y^{\prime }=-5 x -1} \]
✓ Solution by Maple
Time used: 0.562 (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)
\[ y \left (x \right ) = \frac {-\sqrt {-\left (-1+x \right )^{2} c_{1}^{2}+1}+\left (-2 x -1\right ) c_{1}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 53
DSolve[(5*x+2*y[x]+1)+(2*x+y[x]+1)*y'[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*}