7.11.50 problem 52

Internal problem ID [371]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 52
Date solved : Wednesday, February 05, 2025 at 03:26:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)+9*y(x)=sin(3*x),y(x), singsol=all)
 

\[ y = \frac {\left (-x +6 c_1 \right ) \cos \left (3 x \right )}{6}+\sin \left (3 x \right ) c_2 \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 33

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

\[ y(x)\to \left (-\frac {x}{6}+c_1\right ) \cos (3 x)+\frac {1}{36} (1+36 c_2) \sin (3 x) \]