Internal problem ID [12207]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 59.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }-{y^{\prime }}^{2}-y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 20
dsolve(y(x)*diff(y(x),x$2)-diff(y(x),x)^2=diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {{\mathrm e}^{c_{1} \left (c_{2} +x \right )}+1}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.51 (sec). Leaf size: 26
DSolve[y[x]*y''[x]-y'[x]^2==y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1+e^{c_1 (x+c_2)}}{c_1} \\ y(x)\to \text {Indeterminate} \\ \end{align*}