Internal problem ID [3828]
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`]]
\[ \boxed {x \left (1+2 y x \right ) y^{\prime }+\left (1+2 y x -x^{2} y^{2}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \frac {-2+\sqrt {4-2 \ln \left (x \right )+2 c_{1}}}{2 \left (\ln \left (x \right )-c_{1} \right ) x} y \left (x \right ) = -\frac {2+\sqrt {4-2 \ln \left (x \right )+2 c_{1}}}{2 \left (\ln \left (x \right )-c_{1} \right ) x} \end{align*}
✓ Solution by Mathematica
Time used: 0.786 (sec). Leaf size: 79
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 {x}{-2 x^2+\frac {\sqrt {x (-2 \log (x)+4+c_1)}}{\sqrt {\frac {1}{x^3}}}} y(x)\to -\frac {x}{2 x^2+\frac {\sqrt {x (-2 \log (x)+4+c_1)}}{\sqrt {\frac {1}{x^3}}}} y(x)\to 0 \end{align*}