Internal problem ID [11846]
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: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=x \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=x*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = -\left (x -2\right ) {\mathrm e}^{x} \operatorname {expIntegral}_{1}\left (x \right )+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{x}+3+\left (x +2\right ) \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 37
DSolve[y''[x]-2*y'[x]+y[x]==x*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (x-2) \operatorname {ExpIntegralEi}(-x)+(x+2) \log (x)+c_1 e^x+c_2 e^x x+3 \]