# Which method to use?

1. Apr 7, 2005

### estalniath

Hello guys,

Which method can we use to solve the differential equation below?
dy/dx= 1/(xy+x^2y^3)

It doesn't seem to be of any form which I had studied before(linear differential equations,bernoulli,exact differential,homogeneous,seperable equations) for first order differential equations yet it appeared in one of out past examination questions

2. Apr 7, 2005

### dextercioby

It's easy.For me

$$\frac{dy}{dx}=\frac{1}{xy+x^{2}y^{3}}$$

Therefore

$$\frac{dx}{dy}=yx+y^{3}x^{2}$$

Make the substitution

$$x=\frac{1}{u}$$

,under which

$$\frac{dx}{dy}=-\frac{1}{u^{2}}\frac{du}{dy}$$

Therefore the new ODE is

$$-\frac{1}{u^{2}}\frac{du}{dy}=\frac{y}{u}+y^{3}\frac{1}{u^{2}}$$

equivalently

$$\frac{du}{dy}=-yu-y^{3}$$

I trust you can take it from here.It's an nonhomegenous linear ODE...(the homogenous eq is separable).

Daniel.

3. Apr 7, 2005

### estalniath

Wow! That was a fast reply. =) Thank you for replying and how do you type the mathematical equations in between? I don't seem to see any functions in this thread which allows us to type mathematical functions?

4. Apr 7, 2005

### dextercioby

Write formulas in latex code and use preview option for checking it b4 clicking submit.

Daniel.

5. Apr 7, 2005

### estalniath

I see. Thank you for the advice =)

6. Apr 7, 2005