Differentiate the expression $x^2 \tan y$ with respect to $x$, where $y$ is a function of

Question

Differentiate the expression $x^2 \tan y$ with respect to $x$, where $y$ is a function of $x$. Hence solve the differential equation $x^2 \frac{\mathrm{d}y}{\mathrm{d}x} + x \sin 2y = x^3 \cos^2 y$ given that $y(1) = 0$. Give your answer in the form of $y = \mathrm{f}(x)$.

Accepted Answer

(a) $2x\tan y+x^2\sec^2y\,\frac{\mathrm dy}{\mathrm dx}$. (b) $y=\tan^{-1}\left(\frac{x^4-1}{4x^2}\right)$, $x>0$, on the branch through $(1,0)$.

Differential equation initiated by differentiation result

Differential equation initiated by differentiation result

Solution:

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