1.11.17 problem 17

Internal problem ID [338]
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 : 17
Date solved : Tuesday, September 30, 2025 at 03:57:31 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

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

\[ y = \frac {\left (x^{2}+4 c_2 -1\right ) \sin \left (x \right )}{4}-\frac {\cos \left (x \right ) \left (x -4 c_1 \right )}{4} \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to \frac {1}{8} \left (\left (2 x^2-1+8 c_2\right ) \sin (x)-2 (x-4 c_1) \cos (x)\right ) \end{align*}

✓ Sympy. Time used: 0.076 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \left (C_{1} - \frac {x}{4}\right ) \cos {\left (x \right )} + \left (C_{2} + \frac {x^{2}}{4}\right ) \sin {\left (x \right )} \]