65.9.4 problem 16.1 (iv)

Internal problem ID [13783]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 16, Higher order linear equations with constant coefficients. Exercises page 153
Problem number : 16.1 (iv)
Date solved : Tuesday, January 28, 2025 at 06:03:25 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x&={\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 36

dsolve(diff(x(t),t$4)-5*diff(x(t),t$2)+4*x(t)=exp(t),x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {{\mathrm e}^{-2 t} \left (\left (t -6 c_{1} \right ) {\mathrm e}^{3 t}-6 c_{3} {\mathrm e}^{t}-6 c_4 \,{\mathrm e}^{4 t}-6 c_{2} \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 45

DSolve[D[x[t],{t,4}]-5*D[x[t],{t,2}]+4*x[t]==Exp[t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-2 t} \left (c_2 e^t+e^{3 t} \left (-\frac {t}{6}-\frac {1}{36}+c_3\right )+c_4 e^{4 t}+c_1\right ) \]