Differential Eq...

The general solution of the differential equation $$\log _{ e }{ \left( \cfrac { dy }{ dx }  \right)  } =x+y$$ is:

Find the general solution of $$dy=y \sec x dx$$.

The solution of the differential equation $$\dfrac{dx}{x}+\dfrac{dy}{y}=0$$ is

The order of the differential equation $$\left [1 + \left (\dfrac {dy}{dx}\right )^{5}\right ]^{\dfrac {2}{3}} = \dfrac {d^{3}y}{dx^{3}}$$ is:

The general solution of $$\cfrac{dy}{dx}=\cfrac{2x-y}{x+2y}$$ is

If the general solutions of a differential equation is $$(y+c)^2=cx$$, where $$c$$ is an arbitrary constant, then the order and degree of differential equation are:

If $$f(x)$$ and $$g(x)$$ are twice differentiable functions on $$(0, 3)$$ satisfying $$f''(x) = g'', f'(1) = 4, g'(1) = 6, f(2) = 3, g(2) = 9$$, then $$f(1) - g(1)$$ is:

The general solution of the differential equation $$\displaystyle \frac { dy }{ dx } +\frac { 1+\cos { 2y }  }{ 1-\cos { 2x }  } =0$$ is given by:

Which of the following equation is a linear differential equation of order $$3$$ ?

Find a particular solution for the following differential equation.
$$y'-4y'-12y=te^{4t}$$