Internal problem ID [6002]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=x \,{\mathrm e}^{x} \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)+y(x)=x*exp(x)*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (-10 x +22\right ) \cos \left (x \right )^{2}+\left (20 x -4\right ) \sin \left (x \right ) \cos \left (x \right )+5 x -11\right ) {\mathrm e}^{x}}{50}+\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 45
DSolve[y''[x]+y[x]==x*Exp[x]*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{50} e^x (2 (1-5 x) \sin (2 x)+(5 x-11) \cos (2 x))+c_1 \cos (x)+c_2 \sin (x) \]