52.1.31 problem 31

Internal problem ID [10402]
Book : Second order enumerated odes
Section : section 1
Problem number : 31
Date solved : Tuesday, September 30, 2025 at 07:23:06 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)+diff(y(x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -{\mathrm e}^{-x} c_1 +x +c_2 \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 18

ode=D[y[x],{x,2}]+D[y[x],x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x-c_1 e^{-x}+c_2 \end{align*}

✓ Sympy. Time used: 0.067 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} + x \]