8.6.24 problem 24

Internal problem ID [794]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 24
Date solved : Monday, January 27, 2025 at 03:07:15 AM
CAS classification : [_separable]

\begin{align*} 9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(9*x^2*y(x)^2+x^(3/2)*diff(y(x),x) = y(x)^2,y(x), singsol=all)
 

\[ y = \frac {\sqrt {x}}{2+6 x^{2}+c_1 \sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.158 (sec). Leaf size: 34

DSolve[9*x^2*y[x]^2+x^(3/2)*D[y[x],x] == y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sqrt {x}}{6 x^2-c_1 \sqrt {x}+2} \\ y(x)\to 0 \\ \end{align*}