31.1.21 problem 10.3

Internal problem ID [5719]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 10.3
Date solved : Monday, January 27, 2025 at 01:11:26 PM
CAS classification : [_Bernoulli]

\begin{align*} z^{\prime }+2 x z&=2 a \,x^{3} z^{3} \end{align*}

✓ Solution by Maple

Time used: 0.005 (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 \left (x \right ) &= -\frac {2}{\sqrt {4 a \,x^{2}+4 \,{\mathrm e}^{2 x^{2}} c_{1} +2 a}} \\ z \left (x \right ) &= \frac {2}{\sqrt {4 a \,x^{2}+4 \,{\mathrm e}^{2 x^{2}} c_{1} +2 a}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 29

DSolve[D[z[x],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 {1}{2} x^2 \left (a x^2-2\right )} \\ z(x)\to 0 \\ \end{align*}