20.9.18 problem Problem 18

Internal problem ID [3762]
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 18
Date solved : Monday, January 27, 2025 at 08:01:00 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=15*exp(-2*x)*ln(x)+25*cos(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (30 \ln \left (x \right ) x^{2}-45 x^{2}+4 c_{1} x +4 c_{2} \right ) {\mathrm e}^{-2 x}}{4}+3 \cos \left (x \right )+4 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.193 (sec). Leaf size: 54

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==15*Exp[-2*x]*Log[x]+25*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-2 x} \left (-45 x^2+30 x^2 \log (x)+16 e^{2 x} \sin (x)+12 e^{2 x} \cos (x)+4 c_2 x+4 c_1\right ) \]