23.1.396 problem 381

Internal problem ID [5003]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 381
Date solved : Tuesday, September 30, 2025 at 11:20:08 AM
CAS classification : [_linear]

\begin{align*} x^{5} y^{\prime }&=1-3 x^{4} y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=x^5*diff(y(x),x) = 1-3*x^4*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 x -1}{x^{4}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 15

ode=x^5*D[y[x],x]==1-3*x^4*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-1+c_1 x}{x^4} \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**5*Derivative(y(x), x) + 3*x**4*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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