7.7.18 problem 18

Internal problem ID [196]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 18
Date solved : Friday, February 07, 2025 at 08:04:32 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 2 y x^{2}-y^{\prime } x^{3}&=y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

dsolve(2*x^2*y(x)-x^3*diff(y(x),x)=y(x)^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.253 (sec). Leaf size: 43

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

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