It is given that \[\frac{\mathrm{d}y}{\mathrm{d}x} = y\left(2x + \tan^2 x\right) \text{ where}\hspac

Question

It is given that $$\frac{\mathrm{d}y}{\mathrm{d}x} = y\left(2x + \tan^2 x\right) \text{ where}\hspace{0.5em} y \neq 0.$$ Find $y$ in terms of $x$.[5] Hence, given that $y = -2$ when $x = 0$, find the particular solution to the differential equation in part (i).[2]

Accepted Answer

(i) $y=Ae^{x^2-x+\tan x}$, $A\ne0$ (ii) $y=-2e^{x^2-x+\tan x}$

2024 MI PRU2 P1 Q5

2024 MI PRU2 P1 Q5

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