8.11.10 problem 10

Internal problem ID [878]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 10
Date solved : Wednesday, February 05, 2025 at 04:42:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

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

\[ y = \frac {\left (-9 x +18 c_1 +2\right ) \cos \left (3 x \right )}{18}+\frac {\sin \left (3 x \right ) \left (x +3 c_2 \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.167 (sec). Leaf size: 39

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

\[ y(x)\to \left (-\frac {x}{2}+\frac {1}{9}+c_1\right ) \cos (3 x)+\frac {1}{12} (4 x+1+12 c_2) \sin (3 x) \]