Internal problem ID [2781]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y=\frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4}} \]
✓ Solution by Maple
Time used: 0.016 (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: 0.039 (sec). Leaf size: 34
DSolve[y''[x]-10*y'[x]+25*y[x]==2*Exp[5*x]/(4+x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{5 x} \left (x \arctan \left (\frac {x}{2}\right )-\log \left (x^2+4\right )+c_2 x+c_1\right ) \]