Differential Equations Answers

 Eliminate 𝑎, 𝑏 and 𝑐 from 𝑧 = 𝑎(𝑥 + 𝑦) + 𝑏(𝑥 + 𝑦) + 𝑎𝑏𝑡 + 𝑐.

(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

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(t) = c1 sin t + c2 cost