Class 12

Math

Calculus

Differential Equations

The gradient of the curve passing through (4, 0) is given by if the point (5, a) lies on the curve, then the value of a is

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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

The equation of a curve passing through $(2,27 )$ and having gradient $1−x_{2}1 $ at $(x,y)$ is

The rate at which a substance cools in moving air is proportional to the difference between the temperatures of the substance and that of the air. If the temperature of the air is 290 K and the substance cools from 370 K to 330 K in 10 min, when will the temperature be 295 K?

The solutions of (x+y+1) dy=dx are

Find the order and degree (if defined) of the equation: $dx_{3}d_{3}y =xln(dxdy )$

The solution of the differential equation dydx+yxlogy=yx2(logy2) is

Consider a differential equation of order m and degree n. Which one of the following pairs is not feasible?

The solution of the differential equation $x_{2}dxdy cos(x1 )−ysin(x1 )=−1,$ where $y→−1$ as$x→∞$ is