Internal problem ID [2273]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+13 y-4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
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)
\[ y \left (x \right ) = {\mathrm e}^{3 x} \sin \left (2 x \right ) c_{2} +{\mathrm e}^{3 x} \cos \left (2 x \right ) c_{1} +{\mathrm e}^{3 x} \left (\sin \left (2 x \right ) \ln \left (\sec \left (2 x \right )+\tan \left (2 x \right )\right )-1\right ) \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 33
DSolve[y''[x]-6*y'[x]+13*y[x]==4*Exp[3*x]*Sec[2*x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{3 x} (\sin (2 x) (\text {arctanh}(\sin (2 x))+c_1)+c_2 \cos (2 x)-1) \\ \end{align*}