64.12.10 problem 10

Internal problem ID [13514]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 05:50:50 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=x \,{\mathrm e}^{x} \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

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

\[ y = \frac {{\mathrm e}^{x} \left (x^{3} \ln \left (x \right )-\frac {5 x^{3}}{6}+6 c_{1} x +6 c_{2} \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 32

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

\[ y(x)\to \frac {1}{36} e^x \left (x^3 (6 \log (x)-5)+36 c_2 x+36 c_1\right ) \]