75.17.32 problem 582

Internal problem ID [17081]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Superposition principle. Exercises page 137
Problem number : 582
Date solved : Tuesday, January 28, 2025 at 09:51:45 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = \left (c_{1} x +9 x^{2}+c_{2} \right ) {\mathrm e}^{-3 x}+\sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.208 (sec). Leaf size: 86

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==18*Exp[-3*x]+8*Sin[x]+6*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (\int _1^x-2 K[1] \left (3 e^{3 K[1]} \cos (K[1])+4 e^{3 K[1]} \sin (K[1])+9\right )dK[1]+x \int _1^x\left (6 e^{3 K[2]} \cos (K[2])+8 e^{3 K[2]} \sin (K[2])+18\right )dK[2]+c_2 x+c_1\right ) \]