# Linearization of nonlinear non homogenous ODE

1. Jun 23, 2008

### mike79

Hi everybody,
could anyone help me in the linearization of the following non linear non-homogeneous ODE?

A*dy/dt+B*y^(4)=C

where A, B and C are constants. y is a function of t. is it possible to reduce this equation to a Riccati equation? do you know any analytical, approximate or not, methods to solve the equation?

2. Jun 23, 2008

### Defennder

Just to be clear, is this the DE:

$$A \frac{dy}{dt} + By^4 = C$$

If so, then note that you can easily express it as a http://en.wikipedia.org/wiki/Bernoulli_differential_equation" [Broken]and solve it directly without having to approximate it.

Last edited by a moderator: May 3, 2017
3. Jun 27, 2008

### mike79

the DE is right...the BERNOULLI equation is homogeneous and I actually can't tarnsform my equation in a Bernoulli one. can you suggest me how to transform it?

4. Jun 27, 2008

### Defennder

I just had a second look at the DE and realised that there is no need to solve it as a Bernoulli DE. The original DE is separable, though the resulting integral is a little tough to integrate, but certainly doable.

5. Jul 2, 2008

### mike79

i have found in literature the Chini equation, which is similar to the equation I'm trying to solve. unfortunately i can't found the solution. can everyone help me, please?

6. Jul 2, 2008

### HallsofIvy

Defennder has already pointed out that this equation is separable:
$$/frac{Ady}{C- By^4}= dt$$
Integrate both sides, using "partial fractions" on the left.