87.4.10 problem 10

Internal problem ID [23276]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 37
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:28:12 PM
CAS classification : [_linear]

\begin{align*} {\mathrm e}^{x}+x^{3} y^{\prime }+4 x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=exp(x)+x^3*diff(y(x),x)+4*x^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\left (x -1\right ) {\mathrm e}^{x}+c_1}{x^{4}} \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 21

ode=Exp[x]+x^3*D[y[x],x]+4*x^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.162 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), x) + 4*x**2*y(x) + exp(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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