71.3.11 problem 6

Internal problem ID [14290]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 6
Date solved : Monday, March 31, 2025 at 12:15:41 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=diff(y(x),x) = x+y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x -1+{\mathrm e}^{x} c_1 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 28

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

\[ y(x)\to e^x \left (\int _1^xe^{-K[1]} K[1]dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.118 (sec). Leaf size: 10

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

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