29.20.12 problem 557

Internal problem ID [5153]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 557
Date solved : Monday, January 27, 2025 at 10:16:08 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 72

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

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

✓ Solution by Mathematica

Time used: 0.529 (sec). Leaf size: 75

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

\begin{align*} y(x)\to -\frac {3 x^2+\sqrt {-3 x^5+9 x^4+36 c_1 x}}{6 x} \\ y(x)\to \frac {-3 x^2+\sqrt {-3 x^5+9 x^4+36 c_1 x}}{6 x} \\ \end{align*}