Internal problem ID [4108]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-x -\sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+diff(y(x),x)=x+sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{2}-{\mathrm e}^{-x} c_{1}-\frac {\sin \left (2 x \right )}{5}-\frac {\cos \left (2 x \right )}{10}-x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.341 (sec). Leaf size: 41
DSolve[y''[x]+y'[x]==x+Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (x-2) x-\frac {1}{5} \sin (2 x)-\frac {1}{10} \cos (2 x)-c_1 e^{-x}+c_2 \\ \end{align*}