60.2.250 problem 826

Internal problem ID [10837]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 826
Date solved : Tuesday, January 28, 2025 at 05:22:26 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 59

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

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

✓ Solution by Mathematica

Time used: 0.755 (sec). Leaf size: 70

DSolve[D[y[x],x] == (y[x]*(x + 3*y[x]^2 + 3*x*y[x]^2))/(x*(1 + 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^{2 c_1} x}{(x+1)^2}\right )}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2 c_1} x}{(x+1)^2}\right )}}{\sqrt {6}} \\ \end{align*}