89.23.33 problem 37

Internal problem ID [24837]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Miscellaneous Exercises at page 162
Problem number : 37
Date solved : Thursday, October 02, 2025 at 10:48:29 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y&=3 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=1 \\ y^{\prime }\left (\frac {\pi }{2}\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 10

ode:=diff(diff(y(x),x),x)+y(x) = 3; 
ic:=[y(1/2*Pi) = 1, D(y)(1/2*Pi) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -2 \sin \left (x \right )+3 \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 11

ode=D[y[x],{x,2}]+y[x]== 3; 
ic={y[Pi/2]==1,Derivative[1][y][Pi/2] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3-2 \sin (x) \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + Derivative(y(x), (x, 2)) - 3,0) 
ics = {y(pi/2): 1, Subs(Derivative(y(x), x), x, pi/2): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 - 2 \sin {\left (x \right )} \]