For $|x| < 1$, if $x = \cos\left(\frac{1}{a}\log y\right)$, then

The general solution of the given differential equation $dy + (2y - e^{-2x})dx = 0$, is:

[where c is an arbitrary constant]

The sum of order and degree of the differential equation $(x^2\frac{d^2y}{dx^2})^{3/4} = 5(\frac{dy}{dx})^2 - 3$ is equal to

The general solution of the given differential equation $\frac{dy}{dx} = \frac{3e^{2x}+3e^{4x}}{e^{x}+e^{-x}}$ (where C is an arbitrary constant)

Solution of differential equation $x\,dy - y\,dx = 0$ represents:

The integrating factor of the differential equation $y\log_e(10y).\dfrac{dx}{dy}+x=\dfrac{1}{[\log_e(10y)]^2}$, is

Let y(x) be the solution curve of the differential equation $x(1+y^2)dx - y(1+x^2)dy = 0$ and it passes through the point (0, 1), then