Internal problem ID [15351]
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: 582.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y=18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=18*exp(-3*x)+8*sin(x)+6*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} x +9 x^{2}+c_{2} \right ) {\mathrm e}^{-3 x}+\sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.257 (sec). Leaf size: 31
DSolve[y''[x]+6*y'[x]+9*y[x]==18*Exp[-3*x]+8*Sin[x]+6*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (9 x^2+e^{3 x} \sin (x)+c_2 x+c_1\right ) \]