29.20.21 problem 568

Internal problem ID [5162]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 568
Date solved : Monday, January 27, 2025 at 10:16:38 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 47

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

\begin{align*} y \left (x \right ) &= \frac {-2-\sqrt {x^{4}-2 c_{1} +6 x +4}}{x} \\ y \left (x \right ) &= \frac {-2+\sqrt {x^{4}-2 c_{1} +6 x +4}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.681 (sec). Leaf size: 62

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

\begin{align*} y(x)\to -\frac {2 x+\sqrt {x^2 \left (x^4+6 x+4+c_1\right )}}{x^2} \\ y(x)\to \frac {-2 x+\sqrt {x^2 \left (x^4+6 x+4+c_1\right )}}{x^2} \\ \end{align*}