Internal problem ID [2251]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime }-5 \cos \left (3 x \right ) {\mathrm e}^{-2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 73
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)
\[ y \relax (x ) = \frac {667 \,{\mathrm e}^{-52 x} \cos \left (6 x \right ) c_{1}}{1876900}-\frac {39 c_{1} {\mathrm e}^{-52 x} \sin \left (6 x \right )}{469225}+\frac {39 c_{2} {\mathrm e}^{-52 x} \cos \left (6 x \right )}{469225}+\frac {667 \,{\mathrm e}^{-52 x} \sin \left (6 x \right ) c_{2}}{1876900}-\frac {3475 \,{\mathrm e}^{-2 x} \cos \left (3 x \right )}{84184477}-\frac {12240 \,{\mathrm e}^{-2 x} \sin \left (3 x \right )}{84184477}+x c_{3}+c_{4} \]
✓ Solution by Mathematica
Time used: 0.881 (sec). Leaf size: 72
DSolve[y''''[x]+104*y'''[x]+2740*y''[x]==5*Exp[-2*x]*Cos[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_4 x-\frac {5 e^{-2 x} (2448 \sin (3 x)+695 \cos (3 x))}{84184477}+\frac {e^{-52 x} ((156 c_1+667 c_2) \cos (6 x)+(667 c_1-156 c_2) \sin (6 x))}{1876900}+c_3 \\ \end{align*}