Class 12

Math

Calculus

Differential Equations

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

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Determine order and degree (if defined) of differential equations given$yprime+y=e_{x}$

Form the differential equation of the family of hyperbola having foci on x-axis and center at the origin.

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$ycosy=x$ : (y sin y + cos y + x) y = y

Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.

Find the equation of the curve passing through the point (1, 1) whose differential equation is $xdy=(2x_{2}+1)dx(x=0)$.

Find a particular solution of the differential equation $dydx +ycotx=1(x=0)4xcosecx$$(x=0)$, given that $y=0$when $x=2π $

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

The differential equations, find a particular solution satisfying the given condition: $cos(dxdy )=a(a∈R);y=1$