35.6.16 problem 16

Internal problem ID [6166]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 16
Date solved : Monday, January 27, 2025 at 01:43:23 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=30 \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)+9*y(x)=30*sin(3*x),y(x), singsol=all)
 

\[ y = \left (c_1 -5 x \right ) \cos \left (3 x \right )+\sin \left (3 x \right ) c_2 \]

✓ Solution by Mathematica

Time used: 0.107 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]+9*y[x]==30*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (-5 x+c_1) \cos (3 x)+\frac {1}{6} (5+6 c_2) \sin (3 x) \]