Internal problem ID [15378]
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. Initial value problem. Exercises page 140
Problem number: 609.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=4 \cos \left (2 x \right )+\sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=4*cos(2*x)+sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \sin \left (2 x \right ) c_{2} +{\mathrm e}^{-x} \cos \left (2 x \right ) c_{1} +\sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.338 (sec). Leaf size: 30
DSolve[y''[x]+2*y'[x]+5*y[x]==4*Cos[2*x]+Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (c_2 \cos (2 x)+\left (e^x+c_1\right ) \sin (2 x)\right ) \]