If $y = \sin^{-1} x$,then $(1 - x^2) y_2 - x y_1 = $

The second derivative of the function $y = f(x)$ is $f''(x) = 6(x - 1)$. If the graph of the function passes through the point $(2, 1)$ and the equation of the tangent at that point is $y = 3x - 5$,find the equation of the function.

If $y(\theta) = \frac{2 \cos \theta + \cos 2 \theta}{\cos 3 \theta + 4 \cos 2 \theta + 5 \cos \theta + 2}$,then at $\theta = \frac{\pi}{2}$,$y'' + y' + y$ is equal to:

If $y = \sin(\log_e x)$, then $x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx}$ is equal to

If $(a+bx) e^{\frac{y}{x}}=x$,then $x^3 \frac{d^2 y}{d x^2}$ is equal to

If $y = a^x \cdot b^{2x-1}$,then $\frac{d^2 y}{d x^2}$ is equal to