Internal problem ID [13525]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.9 (iv).
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]]
\[ \boxed {y^{\prime \prime }-2 y y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 8
dsolve([diff(y(x),x$2)=2*y(x)*diff(y(x),x),y(0) = 0, D(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = -\tanh \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.684 (sec). Leaf size: 9
DSolve[{y''[x]==2*y[x]*y'[x],{y[0]==0,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\tanh (x) \]