20.9.14 problem Problem 13

Internal problem ID [3758]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.7, The Variation of Parameters Method. page 556
Problem number : Problem 13
Date solved : Monday, January 27, 2025 at 07:59:59 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=4*exp(x)*x^(-3)*ln(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (c_{1} x^{2}+c_{2} x +2 \ln \left (x \right )+3\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 28

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==4*Exp[x]*x^(-3)*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x \left (c_2 x^2+2 \log (x)+c_1 x+3\right )}{x} \]