Internal problem ID [2300]
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: 28.
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]]
\[ \boxed {\left (y+1\right ) y^{\prime \prime }-3 {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) = -1 y \left (x \right ) = -\frac {\sqrt {-2 c_{1} x -2 c_{2}}-1}{\sqrt {-2 c_{1} x -2 c_{2}}} y \left (x \right ) = -\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: 1.378 (sec). Leaf size: 107
DSolve[(y[x]+1)*y''[x]==3*y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 c_1 x+\sqrt {2} \sqrt {-c_1 (x+c_2)}+2 c_2 c_1}{2 c_1 (x+c_2)} y(x)\to \frac {-2 c_1 x+\sqrt {2} \sqrt {-c_1 (x+c_2)}-2 c_2 c_1}{2 c_1 (x+c_2)} y(x)\to -1 y(x)\to \text {Indeterminate} \end{align*}