Internal problem ID [5186]
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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=\frac {{\mathrm e}^{x}}{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)/x,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{2} +{\mathrm e}^{x} x c_{1} +{\mathrm e}^{x} x \left (-1+\ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 22
DSolve[y''[x]-2*y'[x]+y[x]==Exp[x]/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (x \log (x)+(-1+c_2) x+c_1) \]