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 : Tuesday, March 04, 2025 at 10:58:38 AM
CAS classification : [_separable]

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

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

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

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

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

ode=4*x*y[x]^2+D[y[x],x]==5*x^4*y[x]^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.211 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*x**4*y(x)**2 + 4*x*y(x)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {1}{C_{1} + x^{5} - 2 x^{2}} \]