The general solution of the equation dydx = y2 - x2yx + 1 is
y2 = (1 + x)log(1 + x) - c
y2 = 1 + xlogc1 - x - 1
y2 = 1 - xlogc1 - x - 1
y2 = 1 + xlogc1 + x - 1
The general solution of the differential equation dydx + sinx + y2 = sinx - y2 is
logetany2 = - 2sinx2 + C
logetany4 = 2sinx2 + C
logetany4 = - 2sinx2 + C
If a, b, c are three vectors such that [a b c] = 5, then the value of [a x b, b x c, c x a] is
15
25
20
10
The point of inflection of the function y = ∫0xt2 - 3t + 2dt is
32, 34
- 32, - 34
- 12, - 32
12, 32
The value of integral ∫dxxx2 - a2
c - 1asin-1ax
c - 1acos-1ax
sin-1ax + c
c + 1asin-1ax
A.
Let I = ∫dxxx2 - a2Let, x = 1t∴ dx = - 1t2dt∴ I = ∫- dtt2 . 1t1t22 - a2 = - 1a∫dt1a2 - t2 = 1asin-1t + c = - 1asin-1ax + c = c - 1asin-1ax
The function y specified implicitly by the relation ∫0yetdt + ∫0xcostdt = 0 satisfies the differential equation
e2yd2ydx2 + dydx2 = sinx
eyd2ydx2 + dydx2 = sin2x
ey2d2ydx2 + dydx2 = sinx
eyd2ydx2 + dydx2 = sinx