87.17.17 problem 17

Internal problem ID [23609]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 127
Problem number : 17
Date solved : Thursday, October 02, 2025 at 09:43:26 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 33

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

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

✓ Sympy. Time used: 0.064 (sec). Leaf size: 24

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

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