52.1.33 problem 33

Internal problem ID [10404]
Book : Second order enumerated odes
Section : section 1
Problem number : 33
Date solved : Tuesday, September 30, 2025 at 07:23:08 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = \frac {x^{2}}{2}-{\mathrm e}^{-x} c_1 +c_2 \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {x^2}{2}-c_1 e^{-x}+c_2 \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 14

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

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