80.8.6 problem 6

Internal problem ID [18585]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 12:03:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} v^{\prime \prime }-6 v^{\prime }+13 v&={\mathrm e}^{-2 u} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(v(u),u$2)-6*diff(v(u),u)+13*v(u)=exp(-2*u),v(u), singsol=all)
 

\[ v = \left (c_{1} \cos \left (2 u \right )+c_{2} \sin \left (2 u \right )\right ) {\mathrm e}^{-2 u} {\mathrm e}^{5 u}+\frac {{\mathrm e}^{-2 u}}{29} \]

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 39

DSolve[D[v[u],{u,2}]-6*D[v[u],u]+13*v[u]==Exp[-2*u],v[u],u,IncludeSingularSolutions -> True]
 

\[ v(u)\to \frac {e^{-2 u}}{29}+c_2 e^{3 u} \cos (2 u)+c_1 e^{3 u} \sin (2 u) \]