29.21.9 problem 585

Internal problem ID [5179]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 585
Date solved : Monday, January 27, 2025 at 10:18:00 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (3-2 x^{2} y\right ) y^{\prime }&=4 x -3 y+3 x^{2} y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 49

dsolve(x*(3-2*x^2*y(x))*diff(y(x),x) = 4*x-3*y(x)+3*x^2*y(x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {3+\sqrt {-8 x^{3}+4 c_{1} x +9}}{2 x^{2}} \\ y \left (x \right ) &= \frac {3-\sqrt {-8 x^{3}+4 c_{1} x +9}}{2 x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.791 (sec). Leaf size: 71

DSolve[x(3-2 x^2 y[x])D[y[x],x]==4 x-3 y[x]+3 x^2 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {-3 x+\sqrt {x^2 \left (-8 x^3+4 c_1 x+9\right )}}{2 x^3} \\ y(x)\to \frac {3 x+\sqrt {x^2 \left (-8 x^3+4 c_1 x+9\right )}}{2 x^3} \\ \end{align*}