29.3.28 problem 82

Internal problem ID [4690]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 82
Date solved : Monday, January 27, 2025 at 09:31:47 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.182 (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*}