Internal problem ID [2270]
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 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }+5 y-{\mathrm e}^{2 x} \tan \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=exp(2*x)*tan(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} \sin \relax (x ) c_{2}+{\mathrm e}^{2 x} \cos \relax (x ) c_{1}-{\mathrm e}^{2 x} \cos \relax (x ) \ln \left (\frac {\sin \relax (x )+1}{\cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 55
DSolve[y''[x]-4*y'[x]+5*y[x]==Exp[2*x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} \left (c_1 \sin (x)+\cos (x) \left (\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+c_2\right )\right ) \\ \end{align*}