39.3.3 problem Problem 12.3

Internal problem ID [6529]
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
Date solved : Monday, January 27, 2025 at 02:11:34 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{x}}{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)/x,y(x), singsol=all)
 

\[ y = \left (\ln \left (x \right ) x +x \left (c_1 -1\right )+c_2 \right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==Exp[x]/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (x \log (x)+(-1+c_2) x+c_1) \]