20.7.16 problem Problem 41

Internal problem ID [3731]
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 41
Date solved : Monday, January 27, 2025 at 07:56:49 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime }&=5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 58

dsolve(diff(y(x),x$4)+104*diff(y(x),x$3)+2740*diff(y(x),x$2)=5*exp(-2*x)*cos(3*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (\left (667 c_{1} +156 c_{2} \right ) \cos \left (6 x \right )-156 \sin \left (6 x \right ) \left (c_{1} -\frac {667 c_{2}}{156}\right )\right ) {\mathrm e}^{-52 x}}{1876900}+\frac {5 \left (-695 \cos \left (3 x \right )-2448 \sin \left (3 x \right )\right ) {\mathrm e}^{-2 x}}{84184477}+x c_3 +c_4 \]

✓ Solution by Mathematica

Time used: 2.781 (sec). Leaf size: 82

DSolve[D[y[x],{x,4}]+104*D[y[x],{x,3}]+2740*D[y[x],{x,2}]==5*Exp[-2*x]*Cos[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {12240 e^{-2 x} \sin (3 x)}{84184477}-\frac {3475 e^{-2 x} \cos (3 x)}{84184477}+c_4 x+\frac {(156 c_1+667 c_2) e^{-52 x} \cos (6 x)}{1876900}+\frac {(667 c_1-156 c_2) e^{-52 x} \sin (6 x)}{1876900}+c_3 \]