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Alright, thanks for clarifying that. I was just concerned that the question asked "show", not "prove"... And is this alright as a method? EDIT: nvm haha, just read your above post

Is this correct for part (b)? IG, just regarding your approach, I thought of using induction, but if the question asks to "Show" and not "Prove" so can we still use induction (or is that a HSC thing only)?

Yeah thanks for clarifying that. By doing waay too many exact ODEs (treating y as constant) I completely forgot about that fact. Any thoughts on the other question though?

Woah. Wait: if we integrate both sides wrt x, don't we treat y as a constant?

Yeah it's a weird question...I tried both the substitutions suggested but failed to get to a solution. Did you have a look at this one? I added it later on...

I've got a couple of ODEs too. 1)Use the substitution to solve: xyy''=yy'+x(y')^2;u=y'/y \text{ or }u=\ln y \\\text{2) Suppose that }\alpha(x)\text{ is a solution to the equation }\\ \frac{\mathrm{d^2} u}{\mathrm{d} x^2} +b(x) \frac{\mathrm{d} u}{\mathrm{d} x} +c(x)u=0\\\text{(a) Use the...

First year lol (MATH1251 at UNSW) Thanks for that. Yeah, it's probably just easier to not use the substitution and just solve it like a second order ODE.

Got another ODE: \\\text{Use the substitution }v= \frac{\mathrm{d} y}{\mathrm{d} t} \text{ to solve}\\ \frac{\mathrm{d^2} x}{\mathrm{d} t^2}+\omega ^2x=0.

Oh alright, that makes sense then...

Wait doesn't y approach -K (not K) as t-> infinity, knowing 0<y_0<K

oooohhh, couldn't figure out my mistake yesterday. Thanks so much!

Thanks and sorry for the late reply. Could someone please check my working for this one: In the answers provided, they've got \frac{2x^2}{3} instead of \frac{2x^2}{5}

Got another ODE one... $\noindent A savings account is opened with a deposit of $A$ dollars. At any time $t$ years thereafter, money is being continuously deposited into the account at a rate of $(C+Dt)$ dollars per year. If interest is being paid into the account at a nominal rate of $100R\%$...

Oh and yeah thanks I figured it out...

One of my friends asked me...I have no idea where he got it from...

Alright thanks for that, will look into it tomorrow and will let you know how I went.

I checked but I couldn't find any errors/typos I've made. I think you can assume r to be the highest number of children in one single family.

Thanks $\noindent A certain community is composed of $m$ families, $n_i$ of which have $i$ children, $ \sum_{n=i}^{r}n_i=m$. If one of the families is randomly chosen, let $X$ denote the number of children in that family. If one of the $ \sum_{n=i}^{r}in_i$ children is randomly chosen, let $Y$...

Right, thanks. I know it's a bit off-topic, but do you mind also having a look at my other thread I just created. I think it will be mostly about first year uni probability...

Yeah just realised I did essentially that, I used the substitution provided, rearranged it and somehow forced it into the ODE provided (and I know I wasn't supposed to do this)...But since there are two variables in the substitution u=y-x, do we need to use partial differentiation?