84.14.5 problem 7.13

Internal problem ID [22162]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 7. Integrating factors. Supplementary problems
Problem number : 7.13
Date solved : Thursday, October 02, 2025 at 08:33:04 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y+x^{4} y^{2}+x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=y(x)+x^4*y(x)^2+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3}{\left (x^{3}+3 c_1 \right ) x} \]

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 23

ode=(y[x]+x^4*y[x]^2)+x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3}{x^4+3 c_1 x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.121 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {3}{x \left (C_{1} + x^{3}\right )} \]