Bernouilli ODE (where is my mistake?)

  • Thread starter Thread starter justaboy
  • Start date Start date
  • Tags Tags
    Mistake Ode
justaboy
Messages
13
Reaction score
0
found my mistake... thanks
 
Last edited:
Physics news on Phys.org
justaboy said:

Homework Statement


Solve the ODE
x^2y'+2xy-y^3=0



The Attempt at a Solution



x^2y'+2xy-y^3=0
Substitution:
v=y^-2
V makes the equation linear:
v'-4\frac{v}{x}=-2x^{-2}

I get:

v'+\frac{4}{x} v=-\frac{2}{x^2}
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

How to Approach Solving a Nonlinear Second Order ODE with a Quadratic Term?
Replies
4
Views
1K
Solving a separable matrix ODE.
Replies
3
Views
1K
I When is an ODE (numerically) reversible in time?
Replies
4
Views
2K
Solving a Problem: Have I Made a Mistake or Are the Solutions Wrong?
Replies
4
Views
1K
RLC Circuit Analysis with system of ODEs
Replies
2
Views
2K
Fourier Transformation of ODE
Replies
2
Views
2K
Existence and Uniqueness For ODE
Replies
6
Views
2K
Solve the given differential equation
Replies
3
Views
500
Volume between a region (above x-axis and below parabola) and a surface
Replies
4
Views
2K
Finding a periodic solution to ODE
Replies
16
Views
2K

Hot Threads

Recent Insights

Back
Top