29.20.10 problem 555

Internal problem ID [5151]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 555
Date solved : Monday, January 27, 2025 at 10:15:58 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 63

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

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

✓ Solution by Mathematica

Time used: 1.705 (sec). Leaf size: 135

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

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