60.2.152 problem 728

Internal problem ID [10739]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 728
Date solved : Monday, January 27, 2025 at 09:36:53 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {\left (x^{3}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 58

dsolve(diff(y(x),x) = 1/(6*y(x)^2+x)*(x^3+3*y(x)^2)*y(x)/x,y(x), singsol=all)
 

\[ \frac {y^{2} x}{6 y^{2}+x} = \frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (x^{2} {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )-{\mathrm e}^{\textit {\_Z}} \ln \left (\left ({\mathrm e}^{\textit {\_Z}}+9\right ) x \right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+9\right )}+9\right ) x}{54} \]

✓ Solution by Mathematica

Time used: 3.551 (sec). Leaf size: 77

DSolve[D[y[x],x] == (y[x]*(x^3 + 3*y[x]^2))/(x*(x + 6*y[x]^2)),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{x^2+2 c_1}}{x}\right )}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{x^2+2 c_1}}{x}\right )}}{\sqrt {6}} \\ y(x)\to 0 \\ \end{align*}