Internal problem ID [5342]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page
238
Problem number: 1(e).
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 }-y^{\prime } y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)=y(x)*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {\left (c_{2}+x \right ) \sqrt {2}}{2 c_{1}}\right ) \sqrt {2}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 34
DSolve[y''[x]==y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {2} \sqrt {c_1} \tan \left (\frac {\sqrt {c_1} (x+c_2)}{\sqrt {2}}\right ) \\ \end{align*}