Internal problem ID [11779]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+4 y=\cos \left (4 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 41
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+4*y(x)=cos(4*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right ) c_{2} +{\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right ) c_{1} +\frac {\sin \left (4 x \right )}{26}-\frac {3 \cos \left (4 x \right )}{52} \]
✓ Solution by Mathematica
Time used: 1.15 (sec). Leaf size: 54
DSolve[y''[x]+2*y'[x]+4*y[x]==Cos[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{26} \sin (4 x)-\frac {3}{52} \cos (4 x)+c_2 e^{-x} \cos \left (\sqrt {3} x\right )+c_1 e^{-x} \sin \left (\sqrt {3} x\right ) \]