Internal problem ID [13176]
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: 13.4 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }+{y^{\prime }}^{2}-2 y y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(diff(y(x),x)^2+y(x)*diff(y(x),x$2)=2*y(x)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \sqrt {{\mathrm e}^{2 x} c_{1} +2 c_{2}} y \left (x \right ) = -\sqrt {{\mathrm e}^{2 x} c_{1} +2 c_{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.788 (sec). Leaf size: 38
DSolve[y'[x]^2+y[x]*y''[x]==2*y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sqrt {e^{2 x}+e^{c_1}} y(x)\to c_2 \sqrt {e^{2 x}} \end{align*}