Internal problem ID [15332]
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. Superposition principle. Exercises page 137
Problem number: 563.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=4*exp(-x)+17*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\left (c_{1} +1\right ) \cos \left (2 x \right )+\sin \left (2 x \right ) c_{2} +1\right ) {\mathrm e}^{-x}-4 \cos \left (2 x \right )+\sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.335 (sec). Leaf size: 37
DSolve[y''[x]+2*y'[x]+5*y[x]==4*Exp[-x]+17*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (\left (-4 e^x+c_2\right ) \cos (2 x)+\left (e^x+c_1\right ) \sin (2 x)+1\right ) \]