Internal problem ID [12180]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 128.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 65
dsolve(diff(y(x),x)*diff(y(x),x$3)-3*diff(y(x),x$2)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} y \left (x \right ) = \frac {-c_{2} c_{1} +\sqrt {c_{1}^{2} c_{2}^{2}-2 c_{1} c_{3} -2 c_{1} x}}{c_{1}} y \left (x \right ) = -\frac {c_{2} c_{1} +\sqrt {c_{1}^{2} c_{2}^{2}-2 c_{1} c_{3} -2 c_{1} x}}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.307 (sec). Leaf size: 21
DSolve[y'[x]*y'''[x]-3*(y''[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \sqrt {2 x+c_1}+c_3 \]