75.18.7 problem 596

Internal problem ID [17095]
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. Initial value problem. Exercises page 140
Problem number : 596
Date solved : Tuesday, January 28, 2025 at 09:52:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=10 \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 25

dsolve([diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=10*sin(x),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {3 \,{\mathrm e}^{-3 x}}{5}+{\mathrm e}^{-3 x} x -\frac {3 \cos \left (x \right )}{5}+\frac {4 \sin \left (x \right )}{5} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 33

DSolve[{D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==10*Sin[x],{y[0]==0,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} \left (5 e^{-3 x} x+3 e^{-3 x}+4 \sin (x)-3 \cos (x)\right ) \]