Need help to solve y'=(x^2+y^2)^(3/2)

[pociners]

i need some help to solve this equation..

\frac{dy}{dx}=(x^{2}+y^{2})^{\frac{3}{2}}

thanks.

 

[cepheid]

Welcome to PF

This should be posted in the "Calculus & Beyond" section of the Homework Help forum, and it should be posted using the template for homework help threads which includes:

1. An exact statement of the problem

2. Any equations that might be relevant to solving the problem

3. YOUR ATTEMPT AT A SOLUTION SO FAR

What have you done so far for this problem? Hint: can you think of a coordinate transformation that might help here?

 

[pociners]

I'm sorry if I was in the wrong section. I don't know about that.

I've tried using the coordinate transformation.
I suppose x^{2}+y^{2}=r^{2}
where x=r\cos{\theta} and y=r\sin{\theta}

but I do not know what is the \frac{dy}{dx}?

can you help me with this?

 

[pociners]

double post...

 

[cepheid]

I was thinking you could use the chain rule ie

(dy/dx) = (dy/dr)(dr/dx)

But it's working out to be a bit messy for me. Anyway, see if that helps.

 

[pociners]

I was thinking you could use the chain rule ie

(dy/dx) = (dy/dr)(dr/dx)

But it's working out to be a bit messy for me. Anyway, see if that helps.

i've tried it..but it just added a new problem..
r^{3}=\sin(\theta)\cos(\theta)

then what should i do with this??

 

[darkside00]

just develop a new equation of a circle of r^3, then write a new equation that's solvable