Internal problem ID [10455]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }-2 x^{\prime }-4=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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: 0.013 (sec). Leaf size: 14
DSolve[{x''[t]-2*x'[t]==4,{x[0]==1,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{2 t}-2 t \\ \end{align*}