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
A.
Given y = ∫0xt2 - 3t + 2dt ...iOn dlfferentiating w. r. t. 'x', we get dydx = x2 - 3x + 2 ...iiAgain, on differentiating w.r.t. 'x', we getd2ydx2 = 2x - 3 ...iiiWe know that, at point of inflectond2ydx2 = 0∴ From Eq (iii), we get2x - 3 = 0 ⇒ x = 32Now, we have to check behaviour of d2ydx2 at point x = 32Clearly, as x = 32 sign at d2ydx2 changes∴ 32, 34 is a point of inflection.
The value of integral ∫dxxx2 - a2
c - 1asin-1ax
c - 1acos-1ax
sin-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