Internal problem ID [10578]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page
37
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {3 x +2 y+\left (y+2 x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 49
dsolve((3*x+2*y(x))+(2*x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {-2 x c_{1} -\sqrt {c_{1}^{2} x^{2}+1}}{c_{1}} \\ y \left (x \right ) = \frac {-2 x c_{1} +\sqrt {c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.538 (sec). Leaf size: 79
DSolve[(3*x+2*y[x])+(2*x+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x-\sqrt {x^2+e^{2 c_1}} \\ y(x)\to -2 x+\sqrt {x^2+e^{2 c_1}} \\ y(x)\to -\sqrt {x^2}-2 x \\ y(x)\to \sqrt {x^2}-2 x \\ \end{align*}