71.8.2 problem 2

Internal problem ID [14365]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 2
Date solved : Monday, March 31, 2025 at 12:19:33 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 11

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

\[ y = -x -1+{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 25

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

\[ y(x)\to e^x \int _0^xe^{-K[1]} K[1]dK[1] \]

✓ Sympy. Time used: 0.115 (sec). Leaf size: 8

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

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