8.6.18 problem 18

Internal problem ID [788]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 18
Date solved : Wednesday, February 05, 2025 at 04:09:41 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.184 (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*}