Differential Eq...

Solution of $$\displaystyle \frac { dy }{ dx } =\frac { y\left( x\log { y } -y \right)  }{ x\left( y\log { x } -x \right)  } $$ is:

Through any point $$\left ( x,y \right )$$ of a curve which passes through the origin, lines are drawn parallel to the coordiante axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of 

$$\displaystyle y-x\frac{dy}{dx}=b\left ( 1+x^{2}\frac{dy}{dx} \right ).$$
Solve the above differential  equation.

The differential equation $$\displaystyle \frac{dy}{dx}= \displaystyle \frac{\sqrt{1-y^{2}}}{y}$$ determines a family of circles with:

The general solution of the equation $$\displaystyle \frac { dy }{ dx } =\frac { { x }^{ 2 } }{ { y }^{ 2 } } $$ is:

Find the solution of $$\displaystyle \left ( 3\tan x+4\cot y-7 \right )\sin ^{2}ydx$$ $$\displaystyle -\left ( 4\tan x+7\cot y-5 \right )\cos ^{2}xdy=0$$.

If $$\int_{a}^{x} ty (t) dt = x^{2} + y(x)$$ then y as a function of x is:

Find the curve for which the sum of the lengths of the tangent and subtangent at any of its point is proportional to the product of the coordinates of the point of tangency, the proportionality factor is equal to k.