38.6.53 problem 52 (c)

Internal problem ID [8483]
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 (c)
Date solved : Tuesday, September 30, 2025 at 05:38:02 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 (x_{0} \right )&=y_{0} \\ \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 34

ode:=x*diff(y(x),x)-4*y(x) = x^6*exp(x); 
ic:=[y(x__0) = y__0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (\left (-x_{0}^{5}+x_{0}^{4}\right ) {\mathrm e}^{x_{0}}+\left (x -1\right ) {\mathrm e}^{x} x_{0}^{4}+y_{0} \right ) x^{4}}{x_{0}^{4}} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 35

ode=x*D[y[x],x]-4*y[x]==x^6*Exp[x]; 
ic={y[x0]==y0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^4 \left (e^x (x-1) \text {x0}^4-e^{\text {x0}} (\text {x0}-1) \text {x0}^4+\text {y0}\right )}{\text {x0}^4} \end{align*}

✓ Sympy. Time used: 0.164 (sec). Leaf size: 27

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(x__0): y__0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{4} \left (x e^{x} - x^{0} e^{x^{0}} - e^{x} + e^{x^{0}} + \frac {y^{0}}{\left (x^{0}\right )^{4}}\right ) \]