The solution of the differential equation $\frac{dy}{dx} = \tan \left(\frac{y}{x}\right) + \frac{y}{x}$ is

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

Two aeroplanes $I$ and $II$ bomb a target in succession. The probabilities of $I$ and $II$ scoring a hit are $0.3$ and $0.2$,respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

The slope of the tangent at $(x, y)$ to the curve passing through $(2, 1)$ is $\frac{x^2+y^2}{2xy}$. Find the equation of the curve.

The solution of the equation $\frac{dy}{dx} = \frac{x + y}{x - y}$ is

Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=\frac{4y^3+2yx^2}{3xy^2+x^3}$ with $y(1)=1$. If for some $n \in N$,$y(2) \in [n-1, n)$,then $n$ is equal to...