60.1.181 problem 182

Internal problem ID [10195]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 182
Date solved : Monday, January 27, 2025 at 06:37:31 PM
CAS classification : [_rational, _Riccati]

\begin{align*} x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(x*(x^3-1)*diff(y(x),x) - 2*x*y(x)^2 + y(x) + x^2=0,y(x), singsol=all)
 

\[ y = \frac {\left (x +c_{1} \right ) x}{c_{1} x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.715 (sec). Leaf size: 31

DSolve[x*(x^3-1)*D[y[x],x] - 2*x*y[x]^2 + y[x] + x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x (1+2 c_1 x)}{x^2+2 c_1} \\ y(x)\to x^2 \\ \end{align*}