Class 12

Math

Calculus

Differential Equations

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

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The curve satisfying the equation $dxdy =x(y_{3}−x)y(x+y_{3}) $ and passing through the point $(4,−2)$ is

The expression which is the general solution of the differential equation dydx+x1−x2y=xy√ is

Solve $(dxdy )+(xy )=y_{3}$

Suppose that a mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the diameter of the ball decreases from 2cm to 1cm in 3 months, how long will it take until the ball has practically gone?

The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal (a) is linear (b) is homogeneous of second degree (c) has separable variables (d) is of second order

Find the order and degree (if defined) of the equation: $a=dx_{2}d_{2}y 1[1+(dxdy )_{2}]_{23} ,$ where $a$ is constant

Find the differential equation of all the ellipses whose center is at origin and axis are co-ordinate axis.

The equation of the curve satisfying xdy−ydx=x2−y2−−−−−−√ and y(1)=0 is: