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Differential Equation (Second Order)

Hi,
This is my first post on TSR so I apologise if I've posted this in the wrong place etc but I didn't who where else to turn because I had a problem that I'm stuck on.

I've been trying to find a solution to this differential equation for yy in terms of xx. I've tried a multitude of ways and none of them have quite worked out so any help would be appreciated and it'd be great if you could post a full solution. Here's the equation:

d2ydx2=πy2\frac{d^2y}{dx^2}=\frac{\pi}{y^2}

Thanks in advance,
Nick
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by nickk_harrisonn
Hi,
This is my first post on TSR so I apologise if I've posted this in the wrong place etc but I didn't who where else to turn because I had a problem that I'm stuck on.

I've been trying to find a solution to this differential equation for yy in terms of xx. I've tried a multitude of ways and none of them have quite worked out so any help would be appreciated and it'd be great if you could post a full solution. Here's the equation:

d2ydx2=πy2\frac{d^2y}{dx^2}=\frac{\pi}{y^2}

Thanks in advance,
Nick


it has been a while since I dealt with this kind of non linear stuff but if my memory serves me well you use

dy/dx = p

d2y/dx2 = p dp/dy

and ode becomes separable in p and y

is this any good?
Reply 2
Avatar for TeeEm
TeeEm
19
Original post by nickk_harrisonn
Hi,
This is my first post on TSR so I apologise if I've posted this in the wrong place etc but I didn't who where else to turn because I had a problem that I'm stuck on.

I've been trying to find a solution to this differential equation for yy in terms of xx. I've tried a multitude of ways and none of them have quite worked out so any help would be appreciated and it'd be great if you could post a full solution. Here's the equation:

d2ydx2=πy2\frac{d^2y}{dx^2}=\frac{\pi}{y^2}

Thanks in advance,
Nick


I found two very similar ODEs in terms of technique in my own resources, so the suggestion in my previous post was correct.

I hope you find these 2 questions useful in answering your own.

PDF.pdf


I would be interested to hear if anyone else knows of a different method, because I found hard to believe this is a sixth form type ODE
Thankyou so much, I tried your method and got a answer that looks about right, I've differentiated and inputted boundary counsitions and it's held up so far. The PDF was also huge help, especially with the solutions.
The ODE isn't actually part of my sixth form course, I encountered it while trying to solve a problem to do with gravitation. The only reason I labelled 'sixth form' is because I'm in upper sixth at the moment.
Thanks again for your help!
Reply 4
Avatar for TeeEm
TeeEm
19
Original post by nickk_harrisonn
Thankyou so much, I tried your method and got a answer that looks about right, I've differentiated and inputted boundary counsitions and it's held up so far. The PDF was also huge help, especially with the solutions.
The ODE isn't actually part of my sixth form course, I encountered it while trying to solve a problem to do with gravitation. The only reason I labelled 'sixth form' is because I'm in upper sixth at the moment.
Thanks again for your help!


glad it worked

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