Internal
problem
ID
[8775]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
1.0
Problem
number
:
63
Date
solved
:
Wednesday, March 05, 2025 at 06:47:43 AM
CAS
classification
:
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]
Solve
ode:=y(x)*diff(diff(y(x),x),x) = x; dsolve(ode,y(x), singsol=all);
Maple trace
`Methods for second order ODEs: --- Trying classification methods --- trying 2nd order Liouville trying 2nd order WeierstrassP trying 2nd order JacobiSN differential order: 2; trying a linearization to 3rd order trying 2nd order ODE linearizable_by_differentiation trying 2nd order, 2 integrating factors of the form mu(x,y) trying differential order: 2; missing variables -> trying 2nd order, dynamical_symmetries, fully reducible to Abel through one integrating factor of the form G(x,y)/(1+H(x,y)*y)^2 trying 2nd order, integrating factors of the form mu(x,y)/(y)^n, only the singular cases trying symmetries linear in x and y(x) trying differential order: 2; exact nonlinear trying 2nd order, integrating factor of the form mu(y) trying 2nd order, integrating factor of the form mu(x,y) trying 2nd order, integrating factor of the form mu(x,y)/(y)^n, only the general case trying 2nd order, integrating factor of the form mu(y,y) -> Calling odsolve with the ODE`, -(_y1^3*x-1)*y(x)/(_y1^3*x)+(1/3)*(3*(diff(y(x), x))*x+2*_y1)/(x*_y1^3), y(x)` *** Sublevel 2 ** Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear <- 1st order linear successful trying differential order: 2; mu polynomial in y trying 2nd order, integrating factor of the form mu(x,y) differential order: 2; looking for linear symmetries differential order: 2; found: 1 linear symmetries. Trying reduction of order `, `2nd order, trying reduction of order with given symmetries:`[x, 3/2*y]
ode=y[x]*D[y[x],{x,2}]==x; ic={}; DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Not solved
from sympy import * x = symbols("x") y = Function("y") ode = Eq(-x + y(x)*Derivative(y(x), (x, 2)),0) ics = {} dsolve(ode,func=y(x),ics=ics)
NotImplementedError : solve: Cannot solve -x + y(x)*Derivative(y(x), (x, 2))