Internal problem ID [2840]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 87.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+2 x y \left (1+a x y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 83
dsolve(diff(y(x),x)+2*x*y(x)*(1+a*x*y(x)^2) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2}{\sqrt {{\mathrm e}^{2 x^{2}} a \sqrt {\pi }\, \sqrt {2}\, \erf \left (x \sqrt {2}\right )+4 \,{\mathrm e}^{2 x^{2}} c_{1}-4 a x}} \\ y \relax (x ) = \frac {2}{\sqrt {{\mathrm e}^{2 x^{2}} a \sqrt {\pi }\, \sqrt {2}\, \erf \left (x \sqrt {2}\right )+4 \,{\mathrm e}^{2 x^{2}} c_{1}-4 a x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.558 (sec). Leaf size: 96
DSolve[y'[x]+2 x y[x](1+ a x y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{\sqrt {-4 a x+e^{2 x^2} \left (\sqrt {2 \pi } a \text {Erf}\left (\sqrt {2} x\right )+4 c_1\right )}} \\ y(x)\to \frac {2}{\sqrt {-4 a x+e^{2 x^2} \left (\sqrt {2 \pi } a \text {Erf}\left (\sqrt {2} x\right )+4 c_1\right )}} \\ y(x)\to 0 \\ \end{align*}