20.9.6 problem Problem 6

Internal problem ID [3750]
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
Date solved : Monday, January 27, 2025 at 07:58:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \tan \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=exp(2*x)*tan(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==Exp[2*x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} (\cos (x) (-\text {arctanh}(\sin (x)))+c_2 \cos (x)+c_1 \sin (x)) \]