29.20.18 problem 565

Internal problem ID [5159]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 565
Date solved : Monday, January 27, 2025 at 10:16:33 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 51

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

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

✓ Solution by Mathematica

Time used: 0.619 (sec). Leaf size: 57

DSolve[(1-x^2 y[x])D[y[x],x]+1-x y[x]^2==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*}