Internal problem ID [3319]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 577.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (2 y x +1\right ) y^{\prime }+\left (2+3 y x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 43
dsolve(x*(1+2*x*y(x))*diff(y(x),x)+(2+3*x*y(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-x +\sqrt {x^{2}+4 c_{1} x}}{2 x^{2}} \\ y \relax (x ) = -\frac {x +\sqrt {x^{2}+4 c_{1} x}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.496 (sec). Leaf size: 69
DSolve[x(1+2 x y[x])y'[x]+(2+3 x y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^{3/2}+\sqrt {x^2 (x+4 c_1)}}{2 x^{5/2}} \\ y(x)\to \frac {-x^{3/2}+\sqrt {x^2 (x+4 c_1)}}{2 x^{5/2}} \\ \end{align*}