Internal
problem
ID
[9093]
Book
:
Second
order
enumerated
odes
Section
:
section
1
Problem
number
:
22
Date
solved
:
Wednesday, March 05, 2025 at 07:19:39 AM
CAS
classification
:
[[_2nd_order, _missing_x]]
Solve
Does not support ODE with \({y^{\prime \prime }}^{n}\) where \(n\neq 1\) unless \(1\) is missing which is not the case here.
ode:=diff(diff(y(x),x),x)^2+diff(y(x),x)+y(x) = 0; dsolve(ode,y(x), singsol=all);
Maple trace
`Methods for second order ODEs: *** Sublevel 2 *** Methods for second order ODEs: Successful isolation of d^2y/dx^2: 2 solutions were found. Trying to solve each resulting ODE. *** Sublevel 3 *** 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 `, `-> Computing symmetries using: way = 3 `, `-> Computing symmetries using: way = exp_sym -> Calling odsolve with the ODE`, (diff(_b(_a), _a))*_b(_a)-(-_b(_a)-_a)^(1/2) = 0, _b(_a)` *** Sublevel 4 *** Methods for first order ODEs: --- Trying classification methods --- trying homogeneous types: trying exact Looking for potential symmetries trying an equivalence to an Abel ODE trying 1st order ODE linearizable_by_differentiation -> trying 2nd order, dynamical_symmetries, fully reducible to Abel through one integrating factor of the form G(x,y)/(1+H(x,y) trying 2nd order, integrating factors of the form mu(x,y)/(y)^n, only the singular cases trying differential order: 2; exact nonlinear trying 2nd order, integrating factor of the form mu(x,y) -> trying 2nd order, the S-function method -> trying a change of variables {x -> y(x), y(x) -> x} and re-entering methods for the S-function -> trying 2nd order, the S-function method -> trying 2nd order, No Point Symmetries Class V -> trying 2nd order, No Point Symmetries Class V -> trying 2nd order, No Point Symmetries Class V trying 2nd order, integrating factor of the form mu(x,y)/(y)^n, only the general case -> trying 2nd order, dynamical_symmetries, only a reduction of order through one integrating factor of the form G(x,y)/(1+H(x, solving 2nd order ODE of high degree, Lie methods `, `2nd order, trying reduction of order with given symmetries:`[1, 0]
ode=(D[y[x],{x,2}])^2+D[y[x],x]+y[x]==0; ic={}; DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Not solved
from sympy import * x = symbols("x") y = Function("y") ode = Eq(y(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2))**2,0) ics = {} dsolve(ode,func=y(x),ics=ics)
NotImplementedError : solve: Cannot solve y(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2))**2