32.4.23 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.15, page 90

Internal problem ID [5834]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Exercise 10.15, page 90
Date solved : Monday, January 27, 2025 at 01:20:13 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 51

dsolve((y(x)^2+12*x^2*y(x))+(2*x*y(x)+4*x^3)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.513 (sec). Leaf size: 58

DSolve[(y[x]^2+12*x^2*y[x])+(2*x*y[x]+4*x^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2 x^3+\sqrt {x \left (4 x^5+c_1\right )}}{x} \\ y(x)\to \frac {-2 x^3+\sqrt {x \left (4 x^5+c_1\right )}}{x} \\ \end{align*}