29.6.26 problem 26

Internal problem ID [7311]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 26
Date solved : Tuesday, September 30, 2025 at 04:28:04 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=8 x \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)+y(x) = 8*x*sin(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 54

ode=D[y[x],{x,2}]+y[x]==8*x*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sin (x) \int _1^x4 K[2] \sin (2 K[2])dK[2]+\cos (x) \int _1^x-8 K[1] \sin ^2(K[1])dK[1]+c_1 \cos (x)+c_2 \sin (x) \end{align*}

✓ Sympy. Time used: 0.067 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x*sin(x) + y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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