Class 12

Math

Calculus

Differential Equations

Form the differential equation representing the family of curves $y=as∈(x+b)$, where a, b are arbitrary constants.

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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?

The general solution of the differential equation $dxdy =e_{x+y}$is(A) $e_{x}+e_{−y}=C$ (B) $e_{x}+e_{y}=C$(C) $e_{−x}+e_{y}=C$ (D) $e_{−x}+e_{−y}=C$

Form the differential equation representing the family of curves $y=mx$, where, m is arbitrary constant.

Find the equation of the curve passing through the point $(0,4π )$whose differential equation is $sinxcosydx+cosxsinydy=0$.

The differential equations, find a particular solution satisfying the given condition: $dxdy −3ycotx=sin2x;y=2$when $x=2π $

Find the general solution of the differential equations:$dydx +secxy=tanx(0≤x<2π )$

Determine order and degree (if defined) of differential equations given$(dtds )_{4}+3sdt_{2}d_{2}s =0$

Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.