Internal problem ID [109]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {2 x +3 y+\left (3 x +2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 53
dsolve(2*x+3*y(x)+(3*x+2*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-\frac {3 x c_{1}}{2}-\frac {\sqrt {5 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} \\ y \relax (x ) = \frac {-\frac {3 x c_{1}}{2}+\frac {\sqrt {5 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.443 (sec). Leaf size: 110
DSolve[2*x+3*y[x]+(3*x+2*y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-3 x-\sqrt {5 x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (-3 x+\sqrt {5 x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (-\sqrt {5} \sqrt {x^2}-3 x\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5} \sqrt {x^2}-3 x\right ) \\ \end{align*}