Differential Equation Questions

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 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...

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 ?

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 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

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

Consider the following statements: (a) Mode can be computed from histogram (b) Median is not independent of change of scale (c) Variance is independent of change of origin and scale. Which of these is...

The degree and order of the differential equation of the family of all parabolas whose axis is x-axis, are respectively

The solution of the differential equation (1 + y2) + (x - etan- 1y) = 0, is

The order and degree of the differential equation are

The order and degree of the differential equation are -

If f(x), g(x), h(x) are polynomials of three degree, then φ(x) = is a polynomial of degree (where fn(x) represents nth derivative of f(x))-...

The integrating factor of the differential equation 3x logex + y = e 2 loge x is given by...