Edexcel C4 — Question 5

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
TopicDifferential equations

5. The gradient at any point \(( x , y )\) on a curve is proportional to \(\sqrt { y }\). Given that the curve passes through the point with coordinates \(( 0,4 )\),
  1. show that the equation of the curve can be written in the form $$2 \sqrt { y } = k x + 4$$ where \(k\) is a positive constant. Given also that the curve passes through the point with coordinates ( 2,9 ),
  2. find the equation of the curve in the form \(y = \mathrm { f } ( x )\).
    5. continued