60.2.314 problem 891

Internal problem ID [10901]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 891
Date solved : Tuesday, January 28, 2025 at 05:30:19 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {y^{2} \left (-2 y+2 x^{2}+2 x^{2} y+y x^{4}\right )}{x^{3} \left (x^{2}-y+x^{2} y\right )} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 56

dsolve(diff(y(x),x) = y(x)^2/x^3*(-2*y(x)+2*x^2+2*x^2*y(x)+y(x)*x^4)/(x^2-y(x)+x^2*y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.688 (sec). Leaf size: 106

DSolve[D[y[x],x] == (y[x]^2*(2*x^2 - 2*y[x] + 2*x^2*y[x] + x^4*y[x]))/(x^3*(x^2 - y[x] + x^2*y[x])),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {6 x^2}{6+x^2 \left (-6+\sqrt {6} \sqrt {\frac {1}{x^5}} \sqrt {x^5 (-12 \log (x)+31+6 c_1)}\right )} \\ y(x)\to -\frac {6 x^2}{-6+x^2 \left (6+\sqrt {6} \sqrt {\frac {1}{x^5}} \sqrt {x^5 (-12 \log (x)+31+6 c_1)}\right )} \\ y(x)\to 0 \\ \end{align*}