Internal problem ID [4143]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 8. Special second order equations. Lesson 35. Independent variable x
absent
Problem number: Exercise 35.1, page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.091 (sec). Leaf size: 16
dsolve(diff(y(x),x$2)=2*y(x)*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {c_{2}+x}{c_{1}}\right )}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 24
DSolve[y''[x]==2*y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {c_1} \tan \left (\sqrt {c_1} (x+c_2)\right ) \\ \end{align*}