The general solution of the differential equation xdy - ydx = y²dx is

• $\mathrm{y} = \frac{\mathrm{x}}{\mathrm{C} - \mathrm{x}}$

• $\mathrm{x} = \frac{2\mathrm{y}}{\mathrm{C} + \mathrm{x}}$

• $\mathrm{y} = \left(\mathrm{C} + \mathrm{x}\right)\left(2\mathrm{x}\right)$

• $\mathrm{y} = \frac{2\mathrm{x}}{\mathrm{C} + \mathrm{x}}$

The order of the differential equation ${\left(\frac{{\mathrm{d}}^3\mathrm{y}}{{\mathrm{dx}}^3}\right)}^2 + {\left(\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}\right)}^2 + {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^5$ = 0 is

• 3

• 4

• 1

• 5

The solution of dy/dx + ytan(x) = sec(x), y(0) = 0 is

• ysec(x) = tan(x)

• ytan(x) = sec(x)

• tan(x) = ytan(x)

• xsec(x) = tan(y)

The differential equation for, which y = a cos(x) + b sin(x) is a solution, is :

• $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + \mathrm{y} = 0$

• $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} - \mathrm{y} = 0$

• $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + \left(\mathrm{a} + \mathrm{b}\right)\mathrm{y} = 0$

• $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} = \left(\mathrm{a} + \mathrm{b}\right)\mathrm{y}$

The solution of $\frac{\mathrm{dy}}{\mathrm{dx}} + \mathrm{P}\left(\mathrm{x}\right)\mathrm{y} = 0$ is

• $\mathrm{y} = {\mathrm{ce}}^{\int \mathrm{Pdx}}$

• $\mathrm{y} = {\mathrm{ce}}^{- \int \mathrm{Pdx}}$

• $\mathrm{x} = {\mathrm{ce}}^{- \int \mathrm{Pdy}}$

• $\mathrm{x} = {\mathrm{ce}}^{\int \mathrm{Pdy}}$

The differential equation of the family of lines passing through the origin is :

• $\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}} + \mathrm{y} = 0$

• $\mathrm{x} + \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

• $\frac{\mathrm{dy}}{\mathrm{dx}} = \mathrm{y}$

• $\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}} - \mathrm{y} = 0$

147.

The solution of $\frac{\mathrm{dy}}{\mathrm{dx}} + \mathrm{y} = {\mathrm{e}}^{- \mathrm{x}}$; y(0) = 0 is :

• y = e^{- x}(x - 1)

• y = xe^{- x}

• y = xe^{- x} + 1

• y = (x + 1)e^-x

The degree of the differential equation $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^3 + 6\mathrm{y} = 0$ is :

• 1

• 3

• 2

• 5

The solution of the equation (2y - 1)dx - (2x + 3)dy = 0 is  :

• $\frac{2\mathrm{x} - 1}{2\mathrm{y} + 3} = \mathrm{c}$

• $\frac{2\mathrm{x} + 3}{2\mathrm{y} - 1} = \mathrm{c}$

• $\frac{2\mathrm{x} - 1}{2\mathrm{y} - 1} = \mathrm{c}$

• $\frac{2\mathrm{y} + 1}{2\mathrm{x} - 3} = \mathrm{c}$

Let F denotes the family of ellipses whose centre is at the origin and major axis is the y-axis. Then, equation of the family F is :

• $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + \frac{\mathrm{dy}}{\mathrm{dx}}\left(\mathrm{x}\frac{{\displaystyle \mathrm{dy}}}{{\displaystyle \mathrm{dx}}} - \mathrm{y}\right) = 0$

• $\mathrm{xy}\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + \frac{\mathrm{dy}}{\mathrm{dx}}\left(\mathrm{x}\frac{{\displaystyle \mathrm{dy}}}{{\displaystyle \mathrm{dx}}} - \mathrm{y}\right) = 0$

• $\mathrm{xy}\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + \frac{\mathrm{dy}}{\mathrm{dx}}\left(\mathrm{x}\frac{{\displaystyle \mathrm{dy}}}{{\displaystyle \mathrm{dx}}} - \mathrm{y}\right) = 0$

• $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} - \frac{\mathrm{dy}}{\mathrm{dx}}\left(\mathrm{x}\frac{{\displaystyle \mathrm{dy}}}{{\displaystyle \mathrm{dx}}} - \mathrm{y}\right) = 0$