Internal problem ID [4148]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 8. Special second order equations. Lesson 35. Independent variable x
absent
Problem number: Exercise 35.6, page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {\left (y+1\right ) y^{\prime \prime }-3 \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.065 (sec). Leaf size: 59
dsolve((y(x)+1)*diff(y(x),x$2)=3*(diff(y(x),x))^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -1 \\ y \relax (x ) = -\frac {\sqrt {-2 c_{1} x -2 c_{2}}-1}{\sqrt {-2 c_{1} x -2 c_{2}}} \\ y \relax (x ) = -\frac {\sqrt {-2 c_{1} x -2 c_{2}}+1}{\sqrt {-2 c_{1} x -2 c_{2}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 58
DSolve[(y[x]+1)*y''[x]==3*(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-2+\frac {\sqrt {2}}{\sqrt {-c_1 (x+c_2)}}\right ) \\ y(x)\to \frac {1}{2} \left (-2-\frac {\sqrt {2}}{\sqrt {-c_1 (x+c_2)}}\right ) \\ \end{align*}