Internal problem ID [15220]
Internal file name [OUTPUT/15221_Tuesday_April_23_2024_05_23_37_PM_64086032/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: 363.
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, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]
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 `, `-> Computing symmetries using: way = exp_sym -> Calling odsolve with the ODE`, (diff(diff(_b(_a), _a), _a))*_b(_a)^2+(diff(_b(_a), _a))^2*_b(_a)-3*_a*_b(_a) = 0, _b(_a), HINT = symmetry methods on request `, `2nd order, trying reduction of order with given symmetries:`[_a, 3/2*_b]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 11
dsolve([diff(y(x),x$3)=3*y(x)*diff(y(x),x),y(0) = 1, D(y)(0) = 1, (D@@2)(y)(0) = 3/2],y(x), singsol=all)
\[ y = \frac {4}{\left (x -2\right )^{2}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y'''[x]==3*y[x]*y'[x],{y[0]==1,y'[0]==1,y''[0]==3/2}},y[x],x,IncludeSingularSolutions -> True]
{}