Internal problem ID [2296]
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: 24.
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]]
\[ \boxed {y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime } y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(y(x)*diff(y(x),x$2)+diff(y(x),x)^2=y(x)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \sqrt {2 c_{1} {\mathrm e}^{x}+2 c_{2}} y \left (x \right ) = -\sqrt {2 c_{1} {\mathrm e}^{x}+2 c_{2}} \end{align*}
✓ Solution by Mathematica
Time used: 1.093 (sec). Leaf size: 41
DSolve[y[x]*y''[x]+y'[x]^2==y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sqrt {2 e^x+e^{c_1}} y(x)\to \sqrt {2} c_2 \sqrt {e^x} \end{align*}