15.5.11 problem 11

Internal problem ID [2947]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 11
Date solved : Monday, January 27, 2025 at 07:00:07 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.048 (sec). Leaf size: 45

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

\begin{align*} y &= \frac {x +\sqrt {x^{2}-c_1}}{c_1 x} \\ y &= \frac {x -\sqrt {x^{2}-c_1}}{c_1 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.558 (sec). Leaf size: 77

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

\begin{align*} y(x)\to \frac {1}{x^2+\sqrt {-\frac {1}{x^3}} x^2 \sqrt {-x \left (x^2+c_1\right )}} \\ y(x)\to \frac {x}{x^3+\frac {\sqrt {-x \left (x^2+c_1\right )}}{\sqrt {-\frac {1}{x^3}}}} \\ y(x)\to 0 \\ \end{align*}