Internal problem ID [3283]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 539.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y y^{\prime } x +1-2 x^{3}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(2*x*y(x)*diff(y(x),x)+1-2*x^3-y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {x^{3}+c_{1} x +1} \\ y \relax (x ) = -\sqrt {x^{3}+c_{1} x +1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.261 (sec). Leaf size: 37
DSolve[2 x y[x] y'[x]+1-2 x^3-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x^3+c_1 x+1} \\ y(x)\to \sqrt {x^3+c_1 x+1} \\ \end{align*}