32.8.13 problem Exercise 21.16, page 231

Internal problem ID [5962]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined Coefficients
Problem number : Exercise 21.16, page 231
Date solved : Sunday, March 30, 2025 at 10:28:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=x \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

ode:=diff(diff(y(x),x),x)+4*y(x) = x*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-x^{2}+8 c_1 \right ) \cos \left (2 x \right )}{8}+\frac {\sin \left (2 x \right ) \left (x +16 c_2 \right )}{16} \]

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 38

ode=D[y[x],{x,2}]+4*y[x]==x*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{64} \left (\left (-8 x^2+1+64 c_1\right ) \cos (2 x)+4 (x+16 c_2) \sin (2 x)\right ) \]

✓ Sympy. Time used: 0.140 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*sin(2*x) + 4*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} - \frac {x^{2}}{8}\right ) \cos {\left (2 x \right )} + \left (C_{2} + \frac {x}{16}\right ) \sin {\left (2 x \right )} \]