29.20.7 problem 552

Internal problem ID [5148]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 552
Date solved : Monday, January 27, 2025 at 10:15:47 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 51

dsolve(2*x*(2*x^2+y(x))*diff(y(x),x)+(12*x^2+y(x))*y(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: 0.501 (sec). Leaf size: 58

DSolve[2 x(2 x^2+y[x])D[y[x],x]+(12 x^2+y[x])y[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*}