7.11.10 problem 10

Internal problem ID [331]
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 : 10
Date solved : Wednesday, February 05, 2025 at 03:20:54 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 46

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

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