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1. Solve the following differential equations. (a) dy/dt +(1/t)y = cos(t) +(sin(t)/t) , y(2pie) = 1...

1. Solve the following differential equations.
(a) dy/dt +(1/t)y = cos(t) +(sin(t)/t) , y(2pie) = 1
(b)dy/dx = (2x + xy) / (y^2 + 1)
(c) dy/dx=(2xy^2 +1) / (2x^3y)
(d) dy/dx = y-x-1+(xiy+2) ^(-1)
2. A hollow sphere has a diameter of 8 ft. and is filled half way with water. A circular hole (with a radius of 0.5 in.) is opened at the bottom of the sphere. How long will it take for the sphere to become empty? (hint: Draw a diagram)

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