FP2 Differential Equation

http://i.imgur.com/QzjkXLi.png

Need help with the substitution bit on question 1.

http://i.imgur.com/QzjkXLi.png

Need help with the substitution bit on question 1.

What have you done so far? If you're having problems getting started, try differentiating $z=sinx$ implicitly with respect to y and then rearrange to get an expression for $\frac{dy}{dx}$.

With these questions, it's always a good idea to try to find expressions for the differential parts and then slot them into the equation. For instance, in the equation they've given us, we've got $\frac{dy}{dx}$ and $\frac{d^2y}{dx^2}$ so you should be immediately thinking, "how do I get an expression with $\frac{dy}{dx}$ and $\frac{d^2y}{dx^2}$?". There's no $y$ term in the substitution so a good first step would be differentiating with respect to $y$.

the standard method when you start solving ODEs and they give you a substitution is to

find expressions for dy/dx and d²y/dx² by suitably differentiating your substitution.

I keep getting stuck at the d^2y/dx^2. I get dy/dx=dy/dz*dz/dx. The confusing bit is that when trying to get the second derivative, should i leave the dz/dx in dy/dx as it is or substitute it for cosx?

I keep getting stuck at the d^2y/dx^2. I get dy/dx=dy/dz*dz/dx. The confusing bit is that when trying to get the second derivative, should i leave the dz/dx in dy/dx as it is or substitute it for cosx?

look at a similar question (Q10) in this link

http://madasmaths.com/archive/maths_booklets/further_topics/integration/2nd_order_differential_equations_substitutions.pdf

It'll probably make your life easier if you write it as dy/dx=cosx*dy/dz and then differentiate. You'll find it works out quite neatly. There are no dz/dx terms anywhere in the question but there is cos x, so that's a possible hint that you should exchange the former for the latter.

Thank you very much for the link. It's the exact same question(well the first half anyway)! Made everything really clear.