Internal problem ID [3349]
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]
\[ \boxed {y^{\prime }+2 x y \left (1+a x y^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 75
dsolve(diff(y(x),x)+2*x*y(x)*(1+a*x*y(x)^2) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {2}{\sqrt {\left (a \,\operatorname {erf}\left (\sqrt {2}\, x \right ) \sqrt {\pi }\, \sqrt {2}+4 c_{1} \right ) {\mathrm e}^{2 x^{2}}-4 a x}} \\ y \left (x \right ) &= \frac {2}{\sqrt {\left (a \,\operatorname {erf}\left (\sqrt {2}\, x \right ) \sqrt {\pi }\, \sqrt {2}+4 c_{1} \right ) {\mathrm e}^{2 x^{2}}-4 a x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.561 (sec). Leaf size: 106
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 {\sqrt {2 \pi } a e^{2 x^2} \text {erf}\left (\sqrt {2} x\right )-4 a x+4 c_1 e^{2 x^2}}} \\ y(x)\to \frac {2}{\sqrt {\sqrt {2 \pi } a e^{2 x^2} \text {erf}\left (\sqrt {2} x\right )-4 a x+4 c_1 e^{2 x^2}}} \\ y(x)\to 0 \\ \end{align*}