7.7.19 problem 19

Internal problem ID [197]
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 : 19
Date solved : Friday, February 07, 2025 at 08:07:01 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (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: 0.159 (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*}