Internal problem ID [5484]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.9. Reduction of Order. Page
38
Problem number: 1(a).
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]]
Solve \begin {gather*} \boxed {y y^{\prime \prime }+\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 33
dsolve(y(x)*diff(y(x),x$2)+(diff(y(x),x))^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \sqrt {2 c_{1} x +2 c_{2}} \\ y \relax (x ) = -\sqrt {2 c_{1} x +2 c_{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 20
DSolve[y[x]*y''[x]+(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sqrt {2 x-c_1} \\ \end{align*}