Internal problem ID [15448]
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: 704.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {x^{\prime \prime }+\left (x+2\right ) x^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 32
dsolve(diff(x(t),t$2)+(x(t)+2)*diff(x(t),t)=0,x(t), singsol=all)
\[ x \left (t \right ) = -\frac {\left (\sqrt {2}\, c_{1} -\tanh \left (\frac {\left (t +c_{2} \right ) \sqrt {2}}{2 c_{1}}\right )\right ) \sqrt {2}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 60.064 (sec). Leaf size: 40
DSolve[x''[t]+(x[t]+2)*x'[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -2+\sqrt {2} \sqrt {2+c_1} \tanh \left (\frac {\sqrt {2+c_1} (t+c_2)}{\sqrt {2}}\right ) \]