20.9.8 problem Problem 8

Internal problem ID [3752]
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 8
Date solved : Monday, January 27, 2025 at 07:59:26 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=\frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=2*exp(5*x)/(4+x^2),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{5 x} \left (c_{2} +c_{1} x -\ln \left (x^{2}+4\right )+x \arctan \left (\frac {x}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==2*Exp[5*x]/(4+x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{5 x} \left (x \arctan \left (\frac {x}{2}\right )-\log \left (x^2+4\right )+c_2 x+c_1\right ) \]