Internal problem ID [3320]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 578.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {x \left (2 y x +1\right ) y^{\prime }+\left (1+2 y x -x^{2} y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 59
dsolve(x*(1+2*x*y(x))*diff(y(x),x)+(1+2*x*y(x)-x^2*y(x)^2)*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-2+\sqrt {4-2 \ln \relax (x )+2 c_{1}}}{2 \left (\ln \relax (x )-c_{1}\right ) x} \\ y \relax (x ) = -\frac {2+\sqrt {4-2 \ln \relax (x )+2 c_{1}}}{2 \left (\ln \relax (x )-c_{1}\right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.712 (sec). Leaf size: 78
DSolve[x(1+2 x y[x])y'[x]+(1+2 x y[x]-x^2 y[x]^2)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-2 x+\sqrt {\frac {1}{x^3}} x^2 \sqrt {x (-2 \log (x)+4+c_1)}} \\ y(x)\to -\frac {1}{2 x+\sqrt {\frac {1}{x^3}} x^2 \sqrt {x (-2 \log (x)+4+c_1)}} \\ y(x)\to 0 \\ \end{align*}