66.1.4 problem Problem 4

Internal problem ID [13780]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 4
Date solved : Monday, March 31, 2025 at 08:11:34 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+y&=x^{3} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=x*diff(y(x),x)+y(x) = x^3; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 19

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

\[ y(x)\to \frac {x^3}{4}+\frac {c_1}{x} \]

✓ Sympy. Time used: 0.175 (sec). Leaf size: 10

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

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