Internal problem ID [10823]
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 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }-4 x^{\prime }+4 x-{\mathrm e}^{t}-{\mathrm e}^{2 t}-1=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(diff(x(t),t$2)-4*diff(x(t),t)+4*x(t)=exp(t)+exp(2*t)+1,x(t), singsol=all)
\[ x \left (t \right ) = c_{1} t \,{\mathrm e}^{2 t}+\frac {t^{2} {\mathrm e}^{2 t}}{2}+c_{2} {\mathrm e}^{2 t}+{\mathrm e}^{t}+\frac {1}{4} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 32
DSolve[x''[t]-4*x'[t]+4*x[t]==Exp[t]+Exp[2*t]+1,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{2 t} \left (\frac {t^2}{2}+c_2 t+c_1\right )+e^t+\frac {1}{4} \\ \end{align*}