8.3.11 problem 11

Internal problem ID [687]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 11
Date solved : Wednesday, February 05, 2025 at 03:51:07 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

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

\begin{align*} y &= \frac {1}{\sqrt {-x^{2}+c_1}} \\ y &= -\frac {1}{\sqrt {-x^{2}+c_1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 44

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

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