60.2.277 problem 853

Internal problem ID [10864]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 853
Date solved : Monday, January 27, 2025 at 10:18:08 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {14 y x +12+2 x +x^{3} y^{3}+6 x^{2} y^{2}}{x^{2} \left (y x +2+x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 63

dsolve(diff(y(x),x) = 1/x^2*(14*x*y(x)+12+2*x+x^3*y(x)^3+6*x^2*y(x)^2)/(x*y(x)+2+x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.399 (sec). Leaf size: 84

DSolve[D[y[x],x] == (12 + 2*x + 14*x*y[x] + 6*x^2*y[x]^2 + x^3*y[x]^3)/(x^2*(2 + x + x*y[x])),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x-2 \sqrt {-2 x+c_1}+2}{x \left (-1+\sqrt {-2 x+c_1}\right )} \\ y(x)\to -\frac {x+2 \sqrt {-2 x+c_1}+2}{x+x \sqrt {-2 x+c_1}} \\ y(x)\to -\frac {2}{x} \\ \end{align*}