Internal
problem
ID
[9030]
Book
:
First
order
enumerated
odes
Section
:
section
1
Problem
number
:
46
Date
solved
:
Friday, February 21, 2025 at 09:03:42 PM
CAS
classification
:
[_quadrature]
Solve
Factoring the ode gives these factors
Now each of the above equations is solved in turn.
Solving equation (1)
Solving for \(y\) from
Solving gives \(y = 0\)
Solving equation (2)
Solving for the derivative gives these ODE’s to solve
Now each of the above is solved separately.
Solving Eq. (1)
Since the ode has the form \(y^{\prime }=f(x)\), then we only need to integrate \(f(x)\).
Solving Eq. (2)
Since the ode has the form \(y^{\prime }=f(x)\), then we only need to integrate \(f(x)\).
`Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear <- 1st order linear successful`
Solving time : 0.002
(sec)
Leaf size : 9
dsolve(y(x)*diff(y(x),x)^2 = 0,y(x),singsol=all)
Solving time : 0.003
(sec)
Leaf size : 12
DSolve[{y[x]*(D[y[x],x])^2==0,{}},y[x],x,IncludeSingularSolutions->True]
Solving time : 0.131
(sec)
Leaf size : 3
Python version: 3.13.1 (main, Dec 4 2024, 18:05:56) [GCC 14.2.1 20240910] Sympy version 1.13.3
from sympy import * x = symbols("x") y = Function("y") ode = Eq(y(x)*Derivative(y(x), x)**2,0) ics = {} dsolve(ode,func=y(x),ics=ics)
Eq(y(x), C1)