The differential equation $\frac{dy}{dx} + \frac{x}{y} = 0$, represents the family of curves:

The number of arbitrary constants in the general solution of a differential equation of fourth order is:

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

consider the differential equation $\dfrac{dx}{dy} + Px = Q$, where $P$ and $Q$ are function of $y$. Then

A. Its integrating factor (I.F.) is $e^{\int Pdy}$

B. Its integrating factor (I.F.) is $e^{\int Pdx}$

C. Its solution is given by $x(I.F.) = \int Q(I.F.)dy + C$

D. Its solution is given by $y(I.F.) = \int Q(I.F.)dx + C$

Choose the correct answer from the options given below:

The solution of the differential equation $(x^2 + xy)dy = (x^2 + y^2)dx$ is

The sum of the order and degree of the differential equation representing the family of curves $y = mx + m^4$, where m is arbitrary constant, is

The solution of the differential equation $e^{\frac{dy}{dx}} = x+1$; $y(0)=5$ is