8.6.19 problem 19

Internal problem ID [789]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 19
Date solved : Monday, January 27, 2025 at 03:06:41 AM
CAS classification : [_separable]

\begin{align*} 3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(3*x^5*y(x)^2+x^3*diff(y(x),x) = 2*y(x)^2,y(x), singsol=all)
 

\[ y = \frac {x^{2}}{x^{5}+c_1 \,x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 28

DSolve[3*x^5*y[x]^2+x^3*D[y[x],x] == 2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^2}{x^5-c_1 x^2+1} \\ y(x)\to 0 \\ \end{align*}