60.2.106 problem 682

Internal problem ID [10693]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 682
Date solved : Monday, January 27, 2025 at 09:27:40 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y^{\prime }&=\frac {2 a}{x \left (-y x +2 a x y^{2}-8 a^{2}\right )} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 29

dsolve(diff(y(x),x) = 2*a/x/(-x*y(x)+2*a*x*y(x)^2-8*a^2),y(x), singsol=all)
 

\[ \frac {\left (-x y^{2}+4 a \right ) {\mathrm e}^{-4 a y}+c_{1} x}{x} = 0 \]

✓ Solution by Mathematica

Time used: 0.263 (sec). Leaf size: 39

DSolve[D[y[x],x] == (2*a)/(x*(-8*a^2 - x*y[x] + 2*a*x*y[x]^2)),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {y(x)^2 e^{-4 a y(x)}}{8 a}-\frac {e^{-4 a y(x)}}{2 x}=c_1,y(x)\right ] \]