29.17.14 problem 473

Internal problem ID [5071]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 473
Date solved : Monday, January 27, 2025 at 10:07:44 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 51

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

\begin{align*} y \left (x \right ) &= -\frac {x^{3}}{2}-\frac {\sqrt {x^{6}+12 x^{2}-4 c_{1}}}{2} \\ y \left (x \right ) &= -\frac {x^{3}}{2}+\frac {\sqrt {x^{6}+12 x^{2}-4 c_{1}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.151 (sec). Leaf size: 65

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

\begin{align*} y(x)\to \frac {1}{2} \left (-x^3-\sqrt {x^6+12 x^2+4 c_1}\right ) \\ y(x)\to \frac {1}{2} \left (-x^3+\sqrt {x^6+12 x^2+4 c_1}\right ) \\ \end{align*}