Internal problem ID [2244]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined
Coefficients. page 525
Problem number: Problem 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-5 \cos \left (2 x \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)+9*y(x)=5*cos(2*x),y(0) = 2, D(y)(0) = 3],y(x), singsol=all)
\[ y \relax (x ) = 4 \left (\cos ^{3}\relax (x )\right )+\left (4 \sin \relax (x )+2\right ) \left (\cos ^{2}\relax (x )\right )-3 \cos \relax (x )-\sin \relax (x )-1 \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 18
DSolve[{y''[x]+9*y[x]==5*Cos[2*x],{y[0]==2,y'[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (3 x)+\cos (2 x)+\cos (3 x) \\ \end{align*}