49.11.6 problem 1(f)

Internal problem ID [7670]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 93
Problem number : 1(f)
Date solved : Monday, January 27, 2025 at 03:09:29 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=x \,{\mathrm e}^{x} \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 42

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

\[ y = \frac {\left (\left (-10 x +22\right ) \cos \left (x \right )^{2}+\left (20 x -4\right ) \sin \left (x \right ) \cos \left (x \right )+5 x -11\right ) {\mathrm e}^{x}}{50}+\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 45

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

\[ y(x)\to -\frac {1}{50} e^x (2 (1-5 x) \sin (2 x)+(5 x-11) \cos (2 x))+c_1 \cos (x)+c_2 \sin (x) \]