Internal problem ID [11838]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=x \,{\mathrm e}^{x} \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {\left (\ln \left (x \right ) x^{3}-\frac {5 x^{3}}{6}+6 c_{1} x +6 c_{2} \right ) {\mathrm e}^{x}}{6} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 32
DSolve[y''[x]-2*y'[x]+y[x]==x*Exp[x]*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{36} e^x \left (x^3 (6 \log (x)-5)+36 c_2 x+36 c_1\right ) \]