Maths Core WMA01/WMA02: DIFFERENTIATION EQUATIONS Topical Past Paper Questions

(a) Find $ \int\frac{4x+3}{x} $ dx, x>0 (2) (b) Given that y = 25 at x = 1, solve the differential equation $$ \frac{\mathrm{d}y}{\mathrm{d}x}=\frac{(4x+3)y^{\frac{1}{2}}}{x}\qquad x>0,y>0 $$ giving your answer in the form $ y = [g(x)]^{2} $. (5)

The volume of a spherical balloon of radius $ r $ cm is $ V\text{cm}^3 $, where $ V = \frac{4}{3}\pi r^3 $ (a) Find $ \frac{\mathrm{d}V}{\mathrm{d}r} $ (1) The volume of the balloon increases with time t seconds according to the formula $$ \frac{\mathrm{d}V}{\mathrm{d}t}=\frac{90…

Figure 4 Figure 4 shows a right cylindrical water tank. The diameter of the circular cross section of the tank is 4m and the height is 2.25m. Water is flowing into the tank at a constant rate of $ 0.4\pi \, m^3 \, min^{-1} $. There is a tap at a point T at the base of the tank. W…