Internal problem ID [15305]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 535.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y=10 \,{\mathrm e}^{-2 x} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=10*exp(-2*x)*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\left (c_{2} +5 x \right ) \sin \left (x \right )+\cos \left (x \right ) c_{1} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 34
DSolve[y''[x]+4*y'[x]+5*y[x]==10*Exp[-2*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-2 x} ((5+2 c_2) \cos (x)+2 (5 x+c_1) \sin (x)) \]