29.13.20 problem 374

Internal problem ID [4974]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 374
Date solved : Monday, January 27, 2025 at 10:00:40 AM
CAS classification : [_rational, _Riccati]

\begin{align*} x \left (-x^{3}+1\right ) y^{\prime }&=x^{2}+\left (1-2 y x \right ) y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(x*(-x^3+1)*diff(y(x),x) = x^2+(1-2*x*y(x))*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (x +c_{1} \right ) x}{c_{1} x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.715 (sec). Leaf size: 31

DSolve[x(1-x^3)D[y[x],x]==x^2+(1-2 x y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x (1+2 c_1 x)}{x^2+2 c_1} \\ y(x)\to x^2 \\ \end{align*}