7.4.26 problem 26

Internal problem ID [98]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 26
Date solved : Saturday, March 29, 2025 at 04:31:19 PM
CAS classification : [_linear]

\begin{align*} \frac {1-4 x y^{2}}{x^{\prime }}&=y^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=(1-4*x(y)*y^2)/diff(x(y),y) = y^3; 
dsolve(ode,x(y), singsol=all);
 

\[ x = \frac {y^{2}+2 c_1}{2 y^{4}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 20

ode=(1-4*x[y]*y^2)*1/D[x[y],y]==y^3; 
ic={}; 
DSolve[{ode,ic},x[y],y,IncludeSingularSolutions->True]
 

\[ x(y)\to \frac {y^2+2 c_1}{2 y^4} \]

✓ Sympy. Time used: 0.211 (sec). Leaf size: 12

from sympy import * 
y = symbols("y") 
x = Function("x") 
ode = Eq(-y**3 + (-4*y**2*x(y) + 1)/Derivative(x(y), y),0) 
ics = {} 
dsolve(ode,func=x(y),ics=ics)
 

\[ x{\left (y \right )} = \frac {C_{1} + \frac {y^{2}}{2}}{y^{4}} \]