18.1.1 problem Problem 14.2 (a)

Internal problem ID [3457]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.2 (a)
Date solved : Monday, January 27, 2025 at 07:37:23 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }-x y^{3}&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x)-x*y(x)^3=0,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: 0.184 (sec). Leaf size: 44

DSolve[D[y[x],x]-x*y[x]^3==0,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*}