Differential Eq...

Solution of differential equation $$\left( { 2y+xy }^{ 3 } \right) dx+\left( x{ +x }^{ 2 }{ y }^{ 2 } \right) dy=0$$

The differential equation of all circles in the first quadrant which touch the coordinate axes is of order -

The population  $$p(t)$$  at time  $$t$$  of a certain mouse species satisfies the differential equation  $$\dfrac { d p ( t )  } { d t } = 0.5 p ( t ) - 450.$$  If  $$p ( 0 ) = 850 ,$$  then the time at which the population becomes zero is

General solution of the differential equation $$\frac{{dy}}{{dx}} = 1 + xy$$ is

The solution of the differential equation,
  $$\dfrac{dy}{dx}=(x-y)^2$$, when $$y(1)=1$$, is :

The solution of the differential equation $$\dfrac { dy }{ dx } =\dfrac { xy }{ { x }^{ 2 }+y^{ 2 } } $$ is -

The solution of differential equation  $$\cos ^ { 2 } x \dfrac { d y } { d x } - ( \tan 2 x ) y = \cos ^ { 4 } x , | x | < \dfrac { \pi } { 4 } ,$$  where $$y \left( \dfrac { \pi } { 6 } \right) = \dfrac { 3 \sqrt { 3 } } { 8 }$$

A differential equation associated with the primitive $$y=a+b\ e^{5x}+c\ e^{7x}$$ is

If $$\sqrt { \dfrac { \upsilon  }{ \mu  }  } +\sqrt { \dfrac { \mu  }{ \upsilon  }  } =6$$, then $$\dfrac { d\upsilon  }{ d\mu  } =$$

The number of arbitrary constant in the particular solution of a differential equation is