Internal problem ID [14930]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }-3 x^{\prime }+4 x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(x(t),t$2)-3*diff(x(t),t)+4*x(t)=0,x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{\frac {3 t}{2}} \left (c_{1} \sin \left (\frac {\sqrt {7}\, t}{2}\right )+c_{2} \cos \left (\frac {\sqrt {7}\, t}{2}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 42
DSolve[x''[t]-3*x'[t]+4*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{3 t/2} \left (c_2 \cos \left (\frac {\sqrt {7} t}{2}\right )+c_1 \sin \left (\frac {\sqrt {7} t}{2}\right )\right ) \]