60.2.238 problem 814

Internal problem ID [10825]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 814
Date solved : Tuesday, January 28, 2025 at 05:19:31 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class C`], [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 38

dsolve(diff(y(x),x) = y(x)/x*(-3*x^3*y(x)-3+y(x)^2*x^7)/(x^3*y(x)+1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.776 (sec). Leaf size: 75

DSolve[D[y[x],x] == (y[x]*(-3 - 3*x^3*y[x] + x^7*y[x]^2))/(x*(1 + x^3*y[x])),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x}{-x^4+\frac {\sqrt {x (-2 x+1+c_1)}}{\sqrt {\frac {1}{x^7}}}} \\ y(x)\to -\frac {x}{x^4+\frac {\sqrt {x (-2 x+1+c_1)}}{\sqrt {\frac {1}{x^7}}}} \\ y(x)\to 0 \\ \end{align*}