Internal problem ID [11817]
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: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y={\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=exp(-2*x)*(1+cos(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (2 c_{1} +1\right ) \cos \left (x \right )+2+\left (2 c_{2} +x \right ) \sin \left (x \right )\right ) {\mathrm e}^{-2 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.122 (sec). Leaf size: 35
DSolve[y''[x]+4*y'[x]+5*y[x]==Exp[-2*x]*(1+Cos[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-2 x} ((1+4 c_2) \cos (x)+2 (x+2 c_1) \sin (x)+4) \]