If $f(x) = b e^{ax} + a e^{bx}$,then $f^{\prime \prime}(0)$ is equal to

If $y = \left( \frac{ax + b}{cx + d} \right)^2$, then $2 \frac{dy}{dx} \frac{d^3y}{dx^3}$ is equal to

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

If $x=3 \cos t$ and $y=4 \sin t$,then $\frac{d^2 y}{d x^2}$ at the point $(x_0, y_0)=(\frac{3}{2} \sqrt{2}, 2 \sqrt{2})$ is

$f(x)$ is a twice differentiable function such that $f^{\prime \prime}(x)=-f(x)$ and $f^{\prime}(x)=g(x)$. If $h(x)=(f(x))^2+(g(x))^2$ and $h(1)=2$, then $h(2)=$

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.