Internal problem ID [6831]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing.
EXERCISES Page 324
Problem number: 12.
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_y_y1]]
\[ \boxed {y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 36
dsolve(y(x)*diff(y(x),x$2)+diff(y(x),x)^3-diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \\ y \left (x \right ) &= {\mathrm e}^{\frac {-c_{1} \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {x +c_{2}}{c_{1}}}}{c_{1}}\right )+c_{2} +x}{c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 22.067 (sec). Leaf size: 32
DSolve[y[x]*y''[x]+(y'[x])^3-(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{c_1} W\left (e^{e^{-c_1} \left (x-e^{c_1} c_1+c_2\right )}\right ) \]