Show that the differential equation \(\frac{\mathrm{d}y}{\mathrm{d}x}-y\tan x=2\sin x{{\mathrm{e}}^{

Question

Show that the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x}-y\tan x=2\sin x{{\mathrm{e}}^{\cos x}}$ may be reduced by means of the substitution $y=u\sec x$ to $\frac{\mathrm{d}u}{\mathrm{d}x}=2\sin x\cos x{{\mathrm{e}}^{\cos x}}$. Hence find the general solution of the differential equation, giving your answer in the form $y=\mathrm{f}\left( x \right)$.[5]

Accepted Answer

$y = -2e^{\cos x}(1 - \sec x) + C\sec x$

2016 NYJC MYE P1 Q1

2016 NYJC MYE P1 Q1

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