58.1.40 problem 40

Internal problem ID [9111]
Book : Second order enumerated odes
Section : section 1
Problem number : 40
Date solved : Wednesday, March 05, 2025 at 07:24:06 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 18

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

\[ y(x)\to x+c_1 \cos (x)+c_2 \sin (x)+1 \]

✓ Sympy. Time used: 0.052 (sec). Leaf size: 15

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

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