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Let y=arcsin(x)/sqrt(1-x^2). Show that (1-x^2) y'-xy-1=0, and prove that, for all integers n>=0, (1-x^2)y^{n+2}-(2n+3)xy^{n+1} -(n+1)^2 y^{n}=0. (Superscripts denote repeated differentiation)

This is the first part of a STEP question (STEP 3, 2013, Q1), and is an example of a recurring pattern - "Induction Differential Equation".

The first part is a computation, combining the ...

Answered by Daniel H. • STEP tutor

7841 Views

(3 + root(a))(4 + root(a)) = 17 + k(root(a)) where a and k are positive integers. Find the value of a and the value of k.

Let's open out the bracket using the FOIL method (first, outside, inside, last):

(3 + root(a))(4 + root(a)) = 12 + 3root(a) + 4root(a) + (root(a))² = 12 + 7root(a) + a.

Since the ...

Answered by Abhinav J. • Maths tutor

10203 Views

How should I structure my 8 mark questions to improve my grades?

Hi, Make sure the introduction directly addresses the key words in the question. Define them first them state the link/explanation. Conclusions are only really necessary for “Evaluate” questions in which ...

Answered by Alexandra D. • Psychology tutor

20082 Views

Explain why Clemenceau wanted to treat Germany harshly.

The Treaty of Versailles was an agreement of huge historic importance which, at the time, represented not only an end to the bloodiest conflict in human history, but also arguably set the stage for World ...

Answered by Oliver E. • History tutor

31204 Views

What are some Advantages and Disadvantages of Globalisation?

Globalisation is a process of deeper economic integration between countries and regions of the world that has accelerated in the past 50 years. Globalisation benefits large TNCs such as Nike who can reduc...

Answered by Katy B. • Economics tutor

7320 Views