38.6.31 problem 31

Internal problem ID [8461]
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 : 31
Date solved : Tuesday, September 30, 2025 at 05:37:28 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+y&=4 x +1 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=8 \\ \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 14

ode:=x*diff(y(x),x)+y(x) = 1+4*x; 
ic:=[y(1) = 8]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 x +\frac {5}{x}+1 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 15

ode=x*D[y[x],x]+y[x]==4*x+1; 
ic={y[1]==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x+\frac {5}{x}+1 \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - 4*x + y(x) - 1,0) 
ics = {y(1): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 x + 1 + \frac {5}{x} \]