Internal problem ID [12179]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 127.
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: 0.032 (sec). Leaf size: 20
dsolve(diff(y(x),x$3)=diff(y(x),x$2)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (x +c_{1} \right ) \left (x +c_{1} \right )+c_{1} +x +c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.607 (sec). Leaf size: 24
DSolve[y'''[x]==(y''[x])^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x+c_3 x-(x+c_1) \log (x+c_1)+c_2 \]