66.2.36 problem Problem 51

Internal problem ID [13935]
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
Date solved : Tuesday, January 28, 2025 at 06:09:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 40

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

\[ x \left (t \right ) = \frac {\left (\ln \left (2\right )+5\right )^{2} \left (t^{3}+6 c_{1} t +6 c_{2} \right ) {\mathrm e}^{-5 t}+6 \,2^{t}}{6 \left (\ln \left (2\right )+5\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.239 (sec). Leaf size: 72

DSolve[D[x[t],{t,2}]+10*D[x[t],t]+25*x[t]==2^t+t*Exp[-5*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {e^{-5 t} \left (t^3 \left (25+\log ^2(2)+\log (1024)\right )+3\ 2^{t+1} e^{5 t}+c_2 t \left (150+6 \log ^2(2)+\log (1152921504606846976)\right )+c_1 \left (150+6 \log ^2(2)+\log (1152921504606846976)\right )\right )}{6 (5+\log (2))^2} \]