Northwest regional mock advance level June 2021 further mathematics 2
Northwest regional mock advance level June 2021 further mathematics 2
Use the substitution y = vx , where v is a function of x , to transform the differential equation
x*$L = x‘ + xy + yl
dx
into a differential equation in v and x .
Hence find the solution of this differential equation
given that y — lwhen x = 1 .
(3 marks)
(5 marks)
2. Solve for real x , the equation
3cosh2x = 3 4– sink 2;c . (6 marks)
/
3. Given that „ = f x [ l – x )” (lx ,
where n is a positive integer,
show that
( 71 + 2) / i = nl.1–1 , 71 > 1 . (5 marks)
Hence, evaluate I .x ( l — xj dx . (3 marks
