32.5.7 problem Exercise 11.7, page 97

Internal problem ID [5845]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.7, page 97
Date solved : Monday, January 27, 2025 at 01:20:30 PM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

Time used: 3.133 (sec). Leaf size: 50

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

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