26.8.11 problem Exercise 21.14, page 231

Internal problem ID [7095]
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 : Tuesday, September 30, 2025 at 04:21:23 PM
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: 3.349 (sec). Leaf size: 46

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

\begin{align*} y(x)&\to \int _1^xe^{-K[2]} \left (c_1+\int _1^{K[2]}e^{K[1]} (K[1]+\sin (2 K[1]))dK[1]\right )dK[2]+c_2 \end{align*}

✓ Sympy. Time used: 0.107 (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)
 

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