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 : Monday, January 27, 2025 at 01:28:58 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)+diff(y(x),x)=x+sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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