8.6.14 problem 14

Internal problem ID [784]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 14
Date solved : Wednesday, February 05, 2025 at 03:58:34 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 28

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

\begin{align*} y &= \frac {x}{\sqrt {2 \ln \left (x \right )+c_1}} \\ y &= -\frac {x}{\sqrt {2 \ln \left (x \right )+c_1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 41

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

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