Internal problem ID [12498]
Internal file name [OUTPUT/11151_Monday_October_16_2023_09_54_06_PM_81038991/index.tex]
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.
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: 0.078 (sec). Leaf size: 24
dsolve(diff(y(x),x$3)=diff(y(x),x$2)^2,y(x), singsol=all)
\[ y \left (x \right ) = \left (-c_{1} -x \right ) \ln \left (c_{1} +x \right )+\left (c_{2} +1\right ) x +c_{3} +c_{1} \]
✓ Solution by Mathematica
Time used: 0.607 (sec). Leaf size: 24
DSolve[y'''[x]==(y''[x])^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x+c_3 x-(x+c_1) \log (x+c_1)+c_2 \]