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IAL 2021 Jan Q4

A Level / Edexcel / FP2

IAL 2021 Jan Paper · Question 4

(a) Show that the substitution y2=1zy^2 = \dfrac{1}{z} transforms the differential equation

dydx+2y=3xy3y≠0(I)\begin{align*} \frac{\mathrm{d}y}{\mathrm{d}x} + 2y = 3xy^3 \qquad y \neq 0 \qquad \text{(I)} \end{align*}

into the differential equation

dzdx−4z=−6x(II)\begin{align*} \frac{\mathrm{d}z}{\mathrm{d}x} - 4z = -6x \qquad \text{(II)} \end{align*}
(3)

(b) Obtain the general solution of differential equation (II).

(5)

(c) Hence obtain the general solution of differential equation (I), giving your answer in the form y2=f(x)y^2 = f(x)

(1)