Internal problem ID [11498]
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 2.4.3 Reduction of order. Exercises
page 125
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }-2 a x^{\prime }+a^{2} x=0} \] Given that one solution of the ode is \begin {align*} x_1 &= {\mathrm e}^{t a} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve([diff(x(t),t$2)-2*a*diff(x(t),t)+a^2*x(t)=0,exp(a*t)],singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{a t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 18
DSolve[x''[t]-2*a*x'[t]+a^2*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{a t} (c_2 t+c_1) \]