Internal problem ID [93]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y \left (3 x +y\right )+x \left (x +y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 59
dsolve(y(x)*(3*x+y(x))+x*(x+y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-c_{1} x^{2}-\sqrt {c_{1}^{2} x^{4}+1}}{c_{1} x} \\ y \relax (x ) = \frac {-c_{1} x^{2}+\sqrt {c_{1}^{2} x^{4}+1}}{c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.335 (sec). Leaf size: 93
DSolve[y[x]*(3*x+y[x])+x*(x+y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2+\sqrt {x^4+e^{2 c_1}}}{x} \\ y(x)\to -x+\frac {\sqrt {x^4+e^{2 c_1}}}{x} \\ y(x)\to -\frac {\sqrt {x^4}+x^2}{x} \\ y(x)\to \frac {\sqrt {x^4}}{x}-x \\ \end{align*}