Internal problem ID [10851]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 51.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+10 x^{\prime }+25 x-2^{t}-t \,{\mathrm e}^{-5 t}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 46
dsolve(diff(x(t),t$2)+10*diff(x(t),t)+25*x(t)=2^t+t*exp(-5*t),x(t), singsol=all)
\[ x \left (t \right ) = c_{2} {\mathrm e}^{-5 t}+t \,{\mathrm e}^{-5 t} c_{1} +\frac {t^{3} \left (\ln \left (2\right )+5\right )^{2} {\mathrm e}^{-5 t}+6 \,2^{t}}{6 \left (\ln \left (2\right )+5\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 36
DSolve[x''[t]+10*x'[t]+25*x[t]==2^t+t*Exp[-5*t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {2^t}{(5+\log (2))^2}+e^{-5 t} \left (\frac {t^3}{6}+c_2 t+c_1\right ) \\ \end{align*}