Internal problem ID [2753]
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]]
\[ \boxed {y^{\prime \prime }+9 y=5 \cos \left (2 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.046 (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)
\[ y \left (x \right ) = \sin \left (3 x \right )+\cos \left (3 x \right )+\cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.022 (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]
\[ y(x)\to \sin (3 x)+\cos (2 x)+\cos (3 x) \]