Internal problem ID [11835]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y={\mathrm e}^{-2 x} \sec \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=exp(-2*x)*sec(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (-\ln \left (\sec \left (x \right )\right ) \cos \left (x \right )+c_{1} \cos \left (x \right )+\sin \left (x \right ) \left (c_{2} +x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 28
DSolve[y''[x]+4*y'[x]+5*y[x]==Exp[-2*x]*Sec[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} ((x+c_1) \sin (x)+\cos (x) (\log (\cos (x))+c_2)) \]