78.1.10 problem 1.j

Internal problem ID [20936]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 1, First order ODEs. Problems section 1.5
Problem number : 1.j
Date solved : Thursday, October 02, 2025 at 06:49:36 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 11

ode:=diff(y(x),x)-3*y(x)/x = x^3; 
ic:=[y(1) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \left (x +3\right ) x^{3} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to x^3 (x+3) \end{align*}

✓ Sympy. Time used: 0.146 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = x^{3} \left (x + 3\right ) \]