Second order differential equation help

[apple2357]

I am looking at question 2 which involves substitution, I can do 2(i) & (ii) by converting them into first order using the given substitution, but i don't know what to do about the 'y' in Q2(iii). A hint will do? What do i replace it with?

 

[Deleted member 4993]

I am looking at question 2 which involves substitution, I can do 2(i) & (ii) by converting them into first order using the given substitution, but i don't know what to do about the 'y' in Q2(iii). A hint will do? What do i replace it with?

I cannot read the attachment - too fuzzy. Please post a cleaner "picture".

 

[apple2357]

Sorry thats the only version i have:
Q(2) states:
Use the substition dy/dx=p to solve the following differential equation:

2(iii) d2y/dx2 + y(dy/dx)^3 = 0

 

[Steven G]

Well did you make the recommended substitution? What did you get? Where are you stuck?

By this point you know that the helpers on this forum do not solve problems for anyone. So please post back, show us your work and you'll receive excellent help.

 

[apple2357]

I am stuck at the point where i do not know what to replace the 'y' with? So i am stuck at pretty much the beginning!

if dy/dx=p, then d2y/dx2= dp/dx and (dy/dx)^3 = p^3,
So i have

d2y/dx2+y(dy/dx)^3=0 becomes dp/dx+yp^3=0

Now if that 'y' was an 'x' , i could rearrange or use integrating factor but with a 'y' i am not sure. Those are the questions i can do, this one feels different. The previous questions have x terms and not y terms and i haven't come across an example like this nor searching online did i find one.

Sorry I have tried it, I wasn't expecting anyone to solve it for me ( i don't see the point of that!) but rather help me overcome this particular stumbling block- I am missing something in my understanding or i am approaching it in completely the wrong way but i am not sure what it is.

If you think i am expecting you to do it for me, I am not. But if you feel like I am, then don't worry about it. I will explore other avenues. I am sure i will get there in the end.

 

[apple2357]

Ok, I have resolved it now, i was focusing on the wrong thing to replace ( i.e. y). No need for help. You can close the thread.