The differential equation of all circles which pass through the origin and whose centres lie on yaxis is
If , then solution of above equation is
Differential equation for y = A cos αx + B sin αx where A and B are arbitrary constants is
The integrating factor of the different equation dy/dx ( x log x ) + y = 2 log x is given by:
Solution of is
The solution is
Solution of differential equation xdy – ydx = 0 represents
Integration factor of is
A continuously differentiable function y = f(x) ∈ (0,π ) satisfying y = 1 + y, y (0) = 0 = y(π)is
The solution of is
The primitive of  x , when x < 0 is
If is differentiable at x = 1, then the value of (A + 4B) is
ƒ(x) is continuous A + B = A + 3 – B
⇒ B = 3/2
ƒ(x) is differentiable 2B = 6 + A
⇒ A = –3
A function y = ƒ(x) satisfies the differential equation The value of ƒ"(1) is
ƒ'(x) + x^{2}ƒ(x) = –2x, ƒ(1) = 1
⇒ ƒ'(1) + 1 = –2 ⇒ ƒ'(1) = –3
ƒ''(x) + 2xƒ(x) + x^{2}ƒ'(x) = –2
ƒ''(1) + 2ƒ(1) + ƒ'(1) = –2
ƒ''(1) = 3 – 4 = –1 ⇒ ƒ''(1) = 1
If the foci of the ellipse and the hyperbola coincide, then the value of b^{2} is :
Let f(x) = min. for all x ≤ 1. Then the area bounded by y = f(x) and the xaxis is :
The area bounded by the loop of the curve 4y^{2} = x^{2} (4 – x^{2}) is :
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