38.6.25 problem 25

Internal problem ID [8455]
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 : 25
Date solved : Tuesday, September 30, 2025 at 05:37:21 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=x +5 y \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 15

ode:=diff(y(x),x) = x+5*y(x); 
ic:=[y(0) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {x}{5}-\frac {1}{25}+\frac {76 \,{\mathrm e}^{5 x}}{25} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 29

ode=D[y[x],x]==x+5*y[x]; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{5 x} \left (\int _0^xe^{-5 K[1]} K[1]dK[1]+3\right ) \end{align*}

✓ Sympy. Time used: 0.076 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - 5*y(x) + Derivative(y(x), x),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {x}{5} + \frac {76 e^{5 x}}{25} - \frac {1}{25} \]