60.1.250 problem 251

Internal problem ID [10264]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 251
Date solved : Monday, January 27, 2025 at 06:42:33 PM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 51

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

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

✓ Solution by Mathematica

Time used: 0.632 (sec). Leaf size: 57

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

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