class 12

Math

Calculus

Differential Equations

The differential equation which represents the family of curves $y=c_{1}e_{c_{2}x}$, where $c_{1}andc_{2}$are arbitrary constants, is

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

The differential equations , find the particular solution satisfying the given condition:$[xsin_{2}(xy )−y]dx+xdy=0;y=4π $when x = 1

Show that the family of curves for which the slope of the tangent at any point (x, y) on it is $2xyx_{2}+y_{2} $, is given by $x_{2}−y_{2}=cx$.

Form the differential equation representing the family of curves given by $(x−a)_{2}+2y_{2}=a_{2}$, where a is an arbitrary constant.

Find the particular solution of the differential equation $dxdy =−4xy_{2}$given that $y=1$, when$x=0$.

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$y=1+x_{2} $ : $yprime=1+x_{2}xy $

Show that the differential equation $xcos(xy )dxdy =ycos(xy )+x$is homogeneous and solve it.

The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20, 000 in 1999 and 25000 in the year 2004, what will be the population of the village in 2009?

Find the general solution of the differential equations $dxdy =sin_{−1}x$