6.11 problem 11

Internal problem ID [4309]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number: 11.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+10 y-100 \cos \left (4 x \right )=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 37

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+10*y(x)=100*cos(4*x),y(x), singsol=all)
 

\[ y \relax (x ) = {\mathrm e}^{-x} \sin \left (3 x \right ) c_{2}+{\mathrm e}^{-x} \cos \left (3 x \right ) c_{1}+8 \sin \left (4 x \right )-6 \cos \left (4 x \right ) \]

Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 39

DSolve[y''[x]+2*y'[x]+10*y[x]==100*Cos[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 8 \sin (4 x)-6 \cos (4 x)+e^{-x} (c_2 \cos (3 x)+c_1 \sin (3 x)) \\ \end{align*}