Internal problem ID [3867]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 10.3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {z^{\prime }+2 x z-2 a \,x^{3} z^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
dsolve(diff(z(x),x)+2*x*z(x)=2*a*x^3*z(x)^3,z(x), singsol=all)
\begin{align*} z \relax (x ) = -\frac {2}{\sqrt {4 a \,x^{2}+4 \,{\mathrm e}^{2 x^{2}} c_{1}+2 a}} \\ z \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: 0.033 (sec). Leaf size: 29
DSolve[z'[x]+2*x*z[x]==2*a*x^3*z[x],z[x],x,IncludeSingularSolutions -> True]
\begin{align*} z(x)\to c_1 e^{\frac {a x^4}{2}-x^2} \\ z(x)\to 0 \\ \end{align*}