32.6.18 problem Exercise 12.18, page 103

Internal problem ID [5883]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.18, page 103
Date solved : Monday, January 27, 2025 at 01:23:43 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+8 x^{3} y^{3}+2 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 43

dsolve(diff(y(x),x)+8*x^3*y(x)^3+2*x*y(x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {{\mathrm e}^{2 x^{2}} c_{1} -4 x^{2}-2}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {{\mathrm e}^{2 x^{2}} c_{1} -4 x^{2}-2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 7.443 (sec). Leaf size: 58

DSolve[D[y[x],x]+8*x^3*y[x]^3+2*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {-4 x^2+c_1 e^{2 x^2}-2}} \\ y(x)\to \frac {1}{\sqrt {-4 x^2+c_1 e^{2 x^2}-2}} \\ y(x)\to 0 \\ \end{align*}