Internal problem ID [15447]
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: 703.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {x^{\prime \prime }+x {x^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(x(t),t$2)+x(t)*diff(x(t),t)^2=0,x(t), singsol=all)
\[ x \left (t \right ) = -i \operatorname {RootOf}\left (i \sqrt {2}\, c_{1} t +i \sqrt {2}\, c_{2} -\operatorname {erf}\left (\textit {\_Z} \right ) \sqrt {\pi }\right ) \sqrt {2} \]
✓ Solution by Mathematica
Time used: 1.757 (sec). Leaf size: 34
DSolve[x''[t]+x[t]*x'[t]^2==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -i \sqrt {2} \text {erf}^{-1}\left (i \sqrt {\frac {2}{\pi }} c_1 (t+c_2)\right ) \]