7.11.51 problem 53

Internal problem ID [372]
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 : 53
Date solved : Wednesday, February 05, 2025 at 03:26:16 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: 0.001 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 39

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

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