Internal problem ID [3307]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 565.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (1-y x^{2}\right ) y^{\prime }+1-x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 50
dsolve((1-x^2*y(x))*diff(y(x),x)+1-x*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1+\sqrt {2 c_{1} x^{2}+2 x^{3}+1}}{x^{2}} \\ y \relax (x ) = -\frac {-1+\sqrt {2 c_{1} x^{2}+2 x^{3}+1}}{x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.415 (sec). Leaf size: 55
DSolve[(1-x^2 y[x])y'[x]+1-x y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1-\sqrt {1+x^2 (2 x+c_1)}}{x^2} \\ y(x)\to \frac {1+\sqrt {1+x^2 (2 x+c_1)}}{x^2} \\ \end{align*}