20.9.9 problem Problem 9

Internal problem ID [3753]
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 8.7, The Variation of Parameters Method. page 556
Problem number : Problem 9
Date solved : Monday, January 27, 2025 at 07:59:29 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+13*y(x)=4*exp(3*x)*sec(2*x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{3 x} \left (\sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{1} +\sin \left (2 x \right ) \ln \left (\sec \left (2 x \right )+\tan \left (2 x \right )\right )-1\right ) \]

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+13*y[x]==4*Exp[3*x]*Sec[2*x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} \left (c_2 \cos (2 x)+\sin (2 x) \coth ^{-1}(\sin (2 x))+c_1 \sin (2 x)-1\right ) \]