44.6.25 problem 25

Internal problem ID [7169]
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 : Wednesday, March 05, 2025 at 04:19:46 AM
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: 0.010 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.163 (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)
 

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