Internal problem ID [2988]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 240.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y^{\prime } x -\left (1+x -6 y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve(2*x*diff(y(x),x) = (1+x-6*y(x)^2)*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left ({\mathrm e}^{-x} c_{1}+6\right ) x}}{{\mathrm e}^{-x} c_{1}+6} \\ y \relax (x ) = -\frac {\sqrt {\left ({\mathrm e}^{-x} c_{1}+6\right ) x}}{{\mathrm e}^{-x} c_{1}+6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.665 (sec). Leaf size: 65
DSolve[2 x y'[x]==(1+x-6 y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{x/2} \sqrt {x}}{\sqrt {6 e^x+c_1}} \\ y(x)\to \frac {e^{x/2} \sqrt {x}}{\sqrt {6 e^x+c_1}} \\ y(x)\to 0 \\ \end{align*}