52.1.41 problem 41

Internal problem ID [10412]
Book : Second order enumerated odes
Section : section 1
Problem number : 41
Date solved : Tuesday, September 30, 2025 at 07:23:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y&=x^{2}+x +1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)+y(x) = x^2+x+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (x \right ) c_2 +\cos \left (x \right ) c_1 +x^{2}+x -1 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to x^2+x+c_1 \cos (x)+c_2 \sin (x)-1 \end{align*}

✓ Sympy. Time used: 0.032 (sec). Leaf size: 19

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

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