Internal problem ID [2278]
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 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+y-\frac {4 \,{\mathrm e}^{x} \ln \relax (x )}{x^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=4*exp(x)*x^(-3)*ln(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+x \,{\mathrm e}^{x} c_{1}+\frac {2 \,{\mathrm e}^{x} \ln \relax (x )+3 \,{\mathrm e}^{x}}{x} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 27
DSolve[y''[x]-2*y'[x]+y[x]==4*Exp[x]*x^(-3)*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x (2 \log (x)+x (c_2 x+c_1)+3)}{x} \\ \end{align*}