18.17 problem 17

Internal problem ID [2289]

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: 17.
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: 0.016 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)=y(x)*diff(y(x),x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\tan \left (\frac {\left (c_{2} +x \right ) \sqrt {2}}{2 c_{1}}\right ) \sqrt {2}}{c_{1}} \]

✓ Solution by Mathematica

Time used: 15.535 (sec). Leaf size: 34

DSolve[y''[x]==y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {2} \sqrt {c_1} \tan \left (\frac {\sqrt {c_1} (x+c_2)}{\sqrt {2}}\right ) \]