Internal problem ID [1944]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (x +3 y\right ) y^{\prime }=-3 x} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 53
dsolve((3*x+y(x))+(x+3*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {-c_{1} x -\sqrt {-8 c_{1}^{2} x^{2}+3}}{3 c_{1}} \\ y \left (x \right ) &= \frac {-c_{1} x +\sqrt {-8 c_{1}^{2} x^{2}+3}}{3 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.487 (sec). Leaf size: 119
DSolve[(3*x+y[x])+(x+3*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (-x-\sqrt {-8 x^2+3 e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{3} \left (-x+\sqrt {-8 x^2+3 e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{3} \left (-2 \sqrt {2} \sqrt {-x^2}-x\right ) \\ y(x)\to \frac {1}{3} \left (2 \sqrt {2} \sqrt {-x^2}-x\right ) \\ \end{align*}