Internal problem ID [2791]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=15 \ln \left (x \right ) {\mathrm e}^{-2 x}+25 \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.211 (sec). Leaf size: 54
DSolve[y''[x]+4*y'[x]+4*y[x]==15*Exp[-2*x]*Log[x]+25*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-2 x} \left (-45 x^2+30 x^2 \log (x)+16 e^{2 x} \sin (x)+12 e^{2 x} \cos (x)+4 c_2 x+4 c_1\right ) \]