Differential Eq...

Which of the following differential equations has y = x as one of its particular solution?

The equation of a curve passing through $$\displaystyle \left( 2,\frac { 7 }{ 2 }  \right) $$ and having gradient $$\displaystyle 1-\frac { 1 }{ { x }^{ 2 } } $$ at $$(x,y)$$ is:

Which of the following differential equations has $$y = c_1 e^x + c_2 e^{x}$$ as the general solution?

The solution to the differential equation $$(x + 1) \displaystyle \frac{dy}{dx} - y = e^{3x} (x + 1)^2 $$ is

The solution of differential equation 
$$\displaystyle \frac { dy }{ dx } =-\left( \frac { y+\sin { x }  }{ x }  \right) $$ satisfying condition $$\displaystyle y(0) = 1$$, is

The solution of the equation $$\displaystyle \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } ={ e }^{ x }+{ e }^{ -x }$$ is-
Note : (where c & d are arbitrary constants in the given options)

Solution of the differential equation 
$$\displaystyle \left( 2x-y+2 \right) dx+\left( 4x-2y-1 \right) dy=0$$ is 

Solution of differential equation $$\displaystyle \frac { dx }{ dy } =\tan { x } \left( 1+ysinx \right) $$ is given by -

The general solution of the differential equation $$\dfrac{y\, dx-x\, dy}{y}=0$$ is:

The solution of the differential equation $$\dfrac { dy }{ dx } =\dfrac { x-y+3 }{ 2\left( x-y \right) +5 } $$ is