Internal problem ID [7625]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 44.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+2 a \,x^{3} y^{3}+2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
dsolve(diff(y(x),x) + 2*a*x^3*y(x)^3 + 2*x*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2}{\sqrt {-4 a \,x^{2}+4 \,{\mathrm e}^{2 x^{2}} c_{1}-2 a}} \\ y \relax (x ) = \frac {2}{\sqrt {-4 a \,x^{2}+4 \,{\mathrm e}^{2 x^{2}} c_{1}-2 a}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.454 (sec). Leaf size: 70
DSolve[y'[x] + 2*a*x^3*y[x]^3 + 2*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {-\frac {1}{2} a \left (2 x^2+1\right )+c_1 e^{2 x^2}}} \\ y(x)\to \frac {1}{\sqrt {-\frac {1}{2} a \left (2 x^2+1\right )+c_1 e^{2 x^2}}} \\ y(x)\to 0 \\ \end{align*}