7.7.13 problem 13

Internal problem ID [191]
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 : 13
Date solved : Friday, February 07, 2025 at 08:02:43 AM
CAS classification : [_separable]

\begin{align*} 4 x y^{2}+y^{\prime }&=5 y^{2} x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(4*x*y(x)^2+diff(y(x),x)=5*x^4*y(x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 25

DSolve[4*x*y[x]^2+D[y[x],x]==5*x^4*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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