Differential Equation Questions

Let the population of rabbits surviving at a time t be governed by the differential equation p(t) - 200. If p(0) = 100, then p(t) equals...

The function y = f(x) is the solution of the differential equation in (- 1, 1) satisfying f(0) = 0. Then f(x) dx is...

The sum of the co-efficients of all odd degree terms in the expansion of x+x3-15+x-x3-15, (x > 1) is-...

If x-42x2x2xx-42x2x2xx-4 = (A + Bx) (x - A)2, then the ordered pair (A, B) is equal to :...

Let y(x) be a solution of the differential equation (1 + ex)y′ + yex = 1. If y(0) = 2, then which ofthe following statements is(are) true ?

At present a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by . If the firm employs 25 more workers, then the...

A curve passes through the point Let the slope of the curve at each point (x, y) be . Then the equation of the curve is...

The population p(t) at time t of a certain mousespecies satisfies the differential equation = 0.5 p(t) - 450. If p(0) = 850, then thetime at which the population becomes zero is:...

A spherical balloon is filled with 4500π cubicmeters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters per...

Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation = - k (T - 1), where k > 0 is ...

The order of the differential equations whose general solution is given by y = (c1 + c2) cos(x + c3) - c4ex+c5 where c1, c2, c3, c4, c5, are arbitrary constants, is...

A solution of the differential equation is

The differential equation which represents the family of curves y = c1ec2x, where c1 and c2 arearbitrary constants is

The solution of the differential equation satisfying the condition y (1) = 1 is

The differential equation of all circles passing through the origin and having their centres on the x-axis is

The differential equation whose solution is Ax2 + By2 = 1, where A and B are arbitrary constants is of

The differential equation representing the family of curves y2 = 2c (x + √c), where c > 0, is a parameter, is of order and degree as follows:

If a2 + b2 + c2 = - 2 and f(x) = then f(x) is a polynomial of degree

Find the differential equation for the family of curves $x^2 + y^2 - 2ay = 0$, where $a$ is an arbitrary constant.

The solution of the differential equation y dx + (x + x2y) dy = 0 is