The general solution of the differential equation $100 \frac{d^2 y}{dx^2}-20 \frac{dy}{dx}+y=0$ is

Let $y=y(x), y>0$,be a solution curve of the differential equation $(1+x^2) dy = y(x-y) dx$. If $y(0)=1$ and $y(2\sqrt{2})=\beta$,then

If $-\frac{\pi}{4} < x < \frac{\pi}{4},$ then the general solution of the differential equation $\cos^{2} x \cdot \frac{dy}{dx} - (\tan 2x) y = \cos^{4} x$ is

If $\int\limits_a^x {t\,y(t)dt} = x^2 + y(x)$,then $y$ as a function of $x$ is

Let $y = y(x)$ be the solution of the differential equation $(x^2 - x\sqrt{x^2-1})dy + (y(x - \sqrt{x^2-1}) - x)dx = 0, x \geq 1$. If $y(1) = 1$,then the greatest integer less than or equal to $y(\sqrt{5})$ is . . . . . . .

Let $y(x)$ be the solution of the differential equation $2 x^{2} dy + (e^{y} - 2x) dx = 0$,$x > 0$. If $y(e) = 1$,then $y(1)$ is equal to: