Internal problem ID [4678]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 12. VARIATION OF PARAMETERS. page 104
Problem number: Problem 12.3.
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 {{\mathrm e}^{x}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)/x,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{x} c_{1} x +x \,{\mathrm e}^{x} \left (\ln \relax (x )-1\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 22
DSolve[y''[x]-2*y'[x]+y[x]==Exp[x]/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (x \log (x)+(-1+c_2) x+c_1) \\ \end{align*}