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tank having a capacity of 1000 liters, initially contains 400 liters of sugar water having a concen-
tration of 0.2 Kg of sugar for each liter of water. At time zero, sugar water with a concentration of
50 gm of sugar per liter begins pumped into the tank at a rate of 2 liter per minute. Simultaneously,
a drain is opened at the bottom of the tank so that the volume of the sugar-water solution in the
tank reduces 1 liter per minute. Determine the following:
(1+yz)dx + z(z-x)dy - ( 1 + xy ) dz = 0 verify that the pfaffian differential equation are intergrable and find corresponding integral
(1-x^2)d^2y/dx^2 -2x dy/dx+n(n+1)y=0
(D2-3DD'+2D'2)=e^2x-y+ex+y
A tank having a capacity of 1000 liters, initially contains 400 liters of sugar water having a concen-
tration of 0.2 Kg of sugar for each liter of water. At time zero, sugar water with a concentration of
50 gm of sugar per liter begins pumped into the tank at a rate of 2 liter per minute. Simultaneously,
a drain is opened at the bottom of the tank so that the volume of the sugar-water solution in the
tank reduces 1 liter per minute. Determine the following:
y"− 4y′ + 3y = 0,y( 0 )= 7,y′ (0) = 11
y(t) = c1 sin t + c2 cost
