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) $2x \tan y + x^2 \sec^2 y \frac{\mathrm{d}y}{\mathrm{d}x}$; (b) $y = \arctan \left( \frac{x^2}{4} - \frac{1}{4x^2} \right)$.

Differential equation initiated by differentiation result

Differential equation initiated by differentiation result