Internal problem ID [2282]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+4 y-15 \ln \relax (x ) {\mathrm e}^{-2 x}-25 \cos \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)+4*y(x)=15*exp(-2*x)*ln(x)+25*cos(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{-2 x} x c_{1}+\frac {15 x^{2} \left (\ln \relax (x )-\frac {3}{2}\right ) {\mathrm e}^{-2 x}}{2}+3 \cos \relax (x )+4 \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 45
DSolve[y''[x]+4*y'[x]+4*y[x]==15*Exp[-2*x]*Log[x]+25*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-2 x} \left (-45 x^2+30 x^2 \log (x)+4 c_2 x+4 c_1\right )+4 \sin (x)+3 \cos (x) \\ \end{align*}