Internal problem ID [15208]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 350.
ODE order: 1.
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: 22
dsolve(diff(y(x),x$3)+diff(y(x),x$2)^2=0,y(x), singsol=all)
\[ y = \ln \left (x +c_{1} \right ) \left (x +c_{1} \right )+\left (c_{2} -1\right ) x -c_{1} +c_{3} \]
✓ Solution by Mathematica
Time used: 0.315 (sec). Leaf size: 28
DSolve[y'''[x]+y''[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (-1+c_3) x+(x-c_1) \log (x-c_1)+c_2 \]