Differential Eq...

The differential equation representing a family of circles touching  the $$y$$-axis at the origin is 

Solution of differential equation $$\dfrac{dy}{dx}-2xy=x$$ is

If $$2x = {y^{\dfrac{1}{5}}} + {y^{\dfrac{{ - 1}}{5}}}{\text{and}}\left( {{x^2} - 1} \right)\dfrac{{{d^2}y}}{{d{x^2}}} + \lambda x\dfrac{{dy}}{{dx}} + {\text{ky}} = 0,\;{\text{then}}\;\lambda  + {\text{K}}$$ is equal to.

The solution of $$y d x - x d y + 3 x ^ { 2 } y ^ { 2 } e ^ { x ^ { 3 } } d x = 0$$

The order of the differential equation of all circles having radius $$r$$ is.

The solution of, $$\dfrac{xdy}{x^2 + y^2} = \left(\dfrac{y}{x^2 + y^2} - 1 \right)dx$$, is given by

The solution of the differential equation $$\operatorname { xdy } \left( y ^ { 2 } e ^ { x y } + e ^ { \tfrac { x } { y } } \right) = y d x \left( e ^ { \frac { x } { y } } - y ^ { 2 } e ^ { x y } \right)$$ is-

The solution of the differential equation $$( x \cot y + \log \cos x ) d y$$ $$+ ( \log \sin y - y \tan x ) d x = 0$$ is:-

The solution of the differential equation $$y ^ { 2 } d y = x ( y d x - x d y ) \text { is } y = y ( x )$$. If $$y ( \sqrt { 3 } e ) = e$$ and $$y \left( x _ { 0 } \right) = 1$$ then $$x_0$$ is

The differential equation whose solution is $$y = Ax^{5} + Bx^{4}$$ is