38.6.51 problem 52 (a)

Internal problem ID [8481]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 52 (a)
Date solved : Tuesday, September 30, 2025 at 05:37:58 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-4 y&=x^{6} {\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 16

ode:=x*diff(y(x),x)-4*y(x) = x^6*exp(x); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 19

ode=x*D[y[x],x]-4*y[x]==x^6*Exp[x]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^4 \left (e^x (x-1)+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**6*exp(x) + x*Derivative(y(x), x) - 4*y(x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions