32.5.1 problem Exercise 11.1, page 97

Internal problem ID [5839]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.1, page 97
Date solved : Tuesday, March 04, 2025 at 11:47:50 PM
CAS classification : [_linear]

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

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

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

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

✓ Mathematica. Time used: 0.033 (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: 0.164 (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)
 

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