8.11.30 problem 53

Internal problem ID [898]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 53
Date solved : Wednesday, February 05, 2025 at 04:43:49 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 39

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

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