20.9.13 problem Problem 13

Internal problem ID [3757]
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 07:59:55 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\frac {{\mathrm e}^{m x}}{x^{2}+1} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-2*m*diff(y(x),x)+m^2*y(x)=exp(m*x)/(1+x^2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]-2*m*D[y[x],x]+m^2*y[x]==Exp[m*x]/(1+x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{m x} \left (2 x \arctan (x)-\log \left (x^2+1\right )+2 (c_2 x+c_1)\right ) \]