If f(y) = ey, g(y) = y, y > 0 and F(t) = , then
F(t) = 1 - e- t(1 + t)
F(t) = et - (1 + t)
F(t) = tet
F(t) = te- t
The area bounded by the X - axis, the curve y = f(x) and the lines x = 1, x = b and is equal to for all b > 1, then f(x) is
Let f(x) be a function satisfying f'(x) = f(x) with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x2. Then, the value of the integeral is
Family y = Ax + A3 ofcurve is represented by the differential equation ofdegree
3
2
1
None of these
The degree and order of the differential equation of the family of all parabolas whose axis is X-axis, are respectively
2, 1
1, 2
3, 2
2, 3
B.
1, 2
The equation of parabola whose axis is X-axis, is
y2 = 4ax - 4ax1
On differentiating w.r.t. x, we get
Again differentiating w.r.t., x, we get
From above it is clear that degree and order of differential equation are 1 and 2 respectively.
Solution of the differential equation (x + y - 1)dx + (2x+ 2y - 3)dy = 0
y + x + log (x + y - 2) = c
y + 2x + log (x + y - 2) = c
2y + x + log (x + y - 2) = c
2y + 2x + log (x + y - 2) = c