20.8.2 problem Problem 2

Internal problem ID [3735]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial Solutions. page 529
Problem number : Problem 2
Date solved : Monday, January 27, 2025 at 07:57:00 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=50 \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=50*sin(3*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{-x}-3 \cos \left (3 x \right )-4 \sin \left (3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+y[x]==50*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -3 \cos (3 x)+e^{-x} \left (-4 e^x \sin (3 x)+c_2 x+c_1\right ) \]