7.11.61 problem 64

Internal problem ID [382]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 64
Date solved : Saturday, March 29, 2025 at 04:52:18 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+y(x) = 2*sin(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 27

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

\[ y(x)\to (-x+c_1) \cos (x)+\frac {1}{2} (1+2 c_2) \sin (x) \]

✓ Sympy. Time used: 0.089 (sec). Leaf size: 14

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

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