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`]]
\[ \boxed {3 y+\left (3 x +2 y\right ) y^{\prime }=-2 x} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) = \frac {-\frac {3 c_{1} x}{2}-\frac {\sqrt {5 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} y \left (x \right ) = \frac {-\frac {3 c_{1} x}{2}+\frac {\sqrt {5 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.445 (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*}