Solve the following differential equation:
(x2 − y2) dx + 2xy dy = 0 given that y = 1 when x = 1
( x2 - y2 ) dx + 2xy dy = 0
It is a homogeneous differential equation.
Let y = vx ..........(2)
Substituting (2) and (3) in (1), we get:
Integrating both sides, we get:
It is given that when x = 1, y = 1
(1)2 + (2)2 = C(1)
C = 2
Thus, the required solution is y2 + x2 = 2x.
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes.
Using integration find the area of the region bounded by the parabola y2 = 4x and the circle 4x2 + 4y2 = 9.