63.9.22 problem 5

Internal problem ID [13149]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.3.1 Nonhomogeneous Equations: Undetermined Coefficients. Exercises page 110
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 05:09:21 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-2 x^{\prime }&=4 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 12

dsolve([diff(x(t),t$2)-2*diff(x(t),t)=4,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{2 t}-2 t \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 14

DSolve[{D[x[t],{t,2}]-2*D[x[t],t]==4,{x[0]==1,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{2 t}-2 t \]