3.3 problem Problem 12.3

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*}