Internal problem ID [2291]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 19.
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]]
\[ \boxed {y^{\prime \prime }+y^{\prime } y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+y(x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\tanh \left (\frac {\left (c_{2} +x \right ) \sqrt {2}}{2 c_{1}}\right ) \sqrt {2}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 7.104 (sec). Leaf size: 34
DSolve[y''[x]+y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {2} \sqrt {c_1} \tanh \left (\frac {\sqrt {c_1} (x+c_2)}{\sqrt {2}}\right ) \]