Internal problem ID [4136]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22.14, page 240.
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-{\mathrm e}^{x} \ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)*ln(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{x} c_{1} x +\frac {{\mathrm e}^{x} x^{2} \left (2 \ln \relax (x )-3\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 34
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*}