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determine a unique polynomial f(x) of degree<=3 such that
f(x_0)=1, f'(x_0)=2, f(x_1)=2, f'(x_1)=3 where x_1 - x_0 = h
f(x_0)=1, f'(x_0)=2, f(x_1)=2, f'(x_1)=3 where x_1 - x_0 = h
if the second moment of a poisson distribution is 6, find the probability P(X>=2).
Math
a grocery shop sell milk packets containing half a litre of milk. it makes bulk purchase of the same from the nearby city. every time a purchase is made, it incurs a cost of Rs 50 towards transportation. the daily demand of packets is about 250. the holding cost is Rs 0.10 for a packet per day to preserve it in a refrigerator. determine the optimum quantity of a bulk purchase and a cycle time.
Math
solve the following integer linear programming problem
max 2x_1 + 5x_2 + 7x_3
subject to
4x_1 + 3x_2 + x_3 >= 29
where x_1, x_2 and x_3 are non negative integers
max 2x_1 + 5x_2 + 7x_3
subject to
4x_1 + 3x_2 + x_3 >= 29
where x_1, x_2 and x_3 are non negative integers
Solve the following DEs
(i) [(dy/dx)-1]^2 [(d^2y/dx^2)+1]^2 y= sin^2 (x/2) +e^x +x
(ii) 2x^2y (d^2y/dx^2) + 4y^2 = x^2 (dy/dx)^2 + 2xy (dy/dx)
(i) [(dy/dx)-1]^2 [(d^2y/dx^2)+1]^2 y= sin^2 (x/2) +e^x +x
(ii) 2x^2y (d^2y/dx^2) + 4y^2 = x^2 (dy/dx)^2 + 2xy (dy/dx)
Solve the following IVP
(d^2y)/(dx^2) + (dy)/(dx) - 2y = -6 sin2x -18 cos2x
y(0)=2, y'(0)=2
(d^2y)/(dx^2) + (dy)/(dx) - 2y = -6 sin2x -18 cos2x
y(0)=2, y'(0)=2
Find the integrating factor of the differential equation
(6xy-3y^2+2y) dx + 2(x-y) dy =0
and hence solve it
(6xy-3y^2+2y) dx + 2(x-y) dy =0
and hence solve it
Solve the following equation by changing the independent variable
(1+x^2)^2 y" +2x(1+x^2) y' + 4y=0
(1+x^2)^2 y" +2x(1+x^2) y' + 4y=0
true/false.justify.
The normal form of the differential equation
y" - 4xy' + (4x^2 - 1)y =-3e^x^2 sin2x is
(d^2v/dx^2)+v = -3 sin2x, where v= y e^-x^2
The normal form of the differential equation
y" - 4xy' + (4x^2 - 1)y =-3e^x^2 sin2x is
(d^2v/dx^2)+v = -3 sin2x, where v= y e^-x^2
The electrostatic potential V(x,y) in a rectangular region is governed by the two-
dimensional Laplace equation:
d^2V (x,y)/dx^2 + d^2v (x,y)/dy^2 =0
Determine V(x,y) in a rectangular region 0 ≤ x ≤ 20 and 0 ≤ y ≤ 40 for the following
boundary conditions:
V ,0( y) =V 20( , y) =V(x )0, = 0
and
V (x 40, ) =110V
dimensional Laplace equation:
d^2V (x,y)/dx^2 + d^2v (x,y)/dy^2 =0
Determine V(x,y) in a rectangular region 0 ≤ x ≤ 20 and 0 ≤ y ≤ 40 for the following
boundary conditions:
V ,0( y) =V 20( , y) =V(x )0, = 0
and
V (x 40, ) =110V
