71.1.2 problem 1 (b) (page 9)

Internal problem ID [19178]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 1 (b) (page 9)
Date solved : Thursday, October 02, 2025 at 03:40:09 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Sympy. Time used: 0.062 (sec). Leaf size: 8

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

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