85.1.21 problem 12 (b)

Internal problem ID [22426]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 12 (b)
Date solved : Thursday, October 02, 2025 at 08:39:13 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=1-\cos \left (x \right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x) = 1-cos(x); 
ic:=[y(0) = 0, D(y)(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.041 (sec). Leaf size: 15

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

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