Internal problem ID [15207]
Internal file name [OUTPUT/15208_Tuesday_April_23_2024_04_54_10_PM_64380128/index.tex]
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.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode 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]]
Unable to solve or complete the solution.
Unable to parse ODE.
Maple trace
`Methods for third order ODEs: --- Trying classification methods --- trying 3rd order ODE linearizable_by_differentiation differential order: 3; trying a linearization to 4th order trying differential order: 3; missing variables `, `-> Computing symmetries using: way = 3 -> Calling odsolve with the ODE`, diff(_b(_a), _a) = -_b(_a)^2, _b(_a), HINT = [[1, 0], [_a, -_b]]` *** Sublevel 2 *** symmetry methods on request `, `1st order, trying reduction of order with given symmetries:`[1, 0], [_a, -_b]
✓ 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]
\[ y(x)\to (-1+c_3) x+(x-c_1) \log (x-c_1)+c_2 \]