Internal problem ID [2272]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-10 y^{\prime }+25 y-\frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 38
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)
\[ y \relax (x ) = c_{2} {\mathrm e}^{5 x}+{\mathrm e}^{5 x} x c_{1}+{\mathrm e}^{5 x} \left (x \arctan \left (\frac {x}{2}\right )-\ln \left (x^{2}+4\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 33
DSolve[y''[x]-10*y'[x]+25*y[x]==2*Exp[5*x]/(4+x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{5 x} \left (x \left (\text {ArcTan}\left (\frac {x}{2}\right )+c_2\right )-\log \left (x^2+4\right )+c_1\right ) \\ \end{align*}