Solving a Non-Linear ODE: What Method Should I Use?

lkh1986
Messages
96
Reaction score
0

Homework Statement



Solve y'=x^2+y^2 with initial condition y(0)=1.


Homework Equations


This is a first order ODE.



The Attempt at a Solution


I have tried separable variable, exact, and homogeneous and non-homogeneous, but none of them work. It's neither linear nor Bernoulli.

Any clue on what method have I missed or should I tried? Thanks.
 
Physics news on Phys.org
It is a http://en.wikipedia.org/wiki/Riccati_equation" .
 
Last edited by a moderator:
Metaleer said:
It is a http://en.wikipedia.org/wiki/Riccati_equation" .

Thanks. I will try using some suitable transformation to reduce it to a solvable linear DE. :)
 
Last edited by a moderator:

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

Show that ODE is homogeneous, but I don't think it is
Replies
2
Views
2K
Solving a separable matrix ODE.
Replies
3
Views
1K
Avoid unpleasant integrals in solving IVP
Replies
3
Views
2K
Solving a first order ODE using the Adomian Decomposition method
Replies
7
Views
2K
Solving an ODE by the method of Integrating Factors
Replies
5
Views
2K
Solving system of differential equations using elimination method
Replies
10
Views
1K
Use Wronskian method in solving the given second order differential equation
Replies
7
Views
2K
Solving a Non-Homogeneous Linear Differential Equation
Replies
12
Views
2K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
Replies
7
Views
2K
Find the general solution of this nonlinear ODE: xy' + sin(2y) = x^3*sin^2(y)
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top