39.4.1 problem Problem 12.9

Internal problem ID [6535]
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
Date solved : Monday, January 27, 2025 at 02:11:46 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{x}}{x^{5}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)/x^5,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x} \left (12 c_1 \,x^{4}+12 c_2 \,x^{3}+1\right )}{12 x^{3}} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==Exp[x]/x^5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} e^x \left (\frac {1}{x^3}+12 c_2 x+12 c_1\right ) \]