Internal problem ID [4684]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 12. VARIATION OF PARAMETERS. Supplementary Problems. page
109
Problem number: Problem 12.9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+y-\frac {{\mathrm e}^{x}}{x^{5}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)/x^5,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{x} c_{1} x +\frac {{\mathrm e}^{x}}{12 x^{3}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 25
DSolve[y''[x]-2*y'[x]+y[x]==Exp[x]/x^5,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{12} e^x \left (\frac {1}{x^3}+12 c_2 x+12 c_1\right ) \\ \end{align*}