Internal problem ID [15441]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 16. The method of isoclines for differential
equations of the second order. Exercises page 158
Problem number: 697.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+2 x^{\prime }+6 x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(x(t),t$2)+2*diff(x(t),t)+6*x(t)=0,x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-t} \left (c_{1} \sin \left (\sqrt {5}\, t \right )+c_{2} \cos \left (\sqrt {5}\, t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 34
DSolve[x''[t]+2*x'[t]+6*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-t} \left (c_2 \cos \left (\sqrt {5} t\right )+c_1 \sin \left (\sqrt {5} t\right )\right ) \]