32.8.11 problem Exercise 21.14, page 231

Internal problem ID [5960]
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 21.14, page 231
Date solved : Sunday, March 30, 2025 at 10:28:16 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

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

\[ y = \frac {x^{2}}{2}-{\mathrm e}^{-x} c_1 -\frac {\sin \left (2 x \right )}{5}-\frac {\cos \left (2 x \right )}{10}-x +c_2 \]

✓ Mathematica. Time used: 0.361 (sec). Leaf size: 43

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

\[ y(x)\to \frac {x^2}{2}-x-\frac {1}{5} \sin (2 x)-\frac {1}{10} \cos (2 x)-c_1 e^{-x}+c_2 \]

✓ Sympy. Time used: 0.169 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} + \frac {x^{2}}{2} - x - \frac {\sin {\left (2 x \right )}}{5} - \frac {\cos {\left (2 x \right )}}{10} \]