Internal problem ID [5564]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF VARIATION OF
PARAMETERS. Page 71
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y-{\mathrm e}^{-x} \ln \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=exp(-x)*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} x c_{1} +\frac {x^{2} \left (2 \ln \left (x \right )-3\right ) {\mathrm e}^{-x}}{4} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 36
DSolve[y''[x]+2*y'[x]+y[x]==Exp[-x]*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-x} \left (-3 x^2+2 x^2 \log (x)+4 c_2 x+4 c_1\right ) \\ \end{align*}