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# Polar Coordinates : Solving Derivatives and Circuit Problem

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Please see the attached file for full problem description.

(a) By making the substitution y = z/x^4, or otherwise, reduce the equation
dy/dx +4y/x =sinx/x2

to an equation in which the variables are separable.

Solve the equation if y = 0 when x = pi/2

(b) In a circuit
di/dt=K(E-Ri)

and i=0 when t=0.

Find i in terms of t and deduce that as t ?>infinity i ?> I = E/R (E,R, K positive constants).
If i=2/3I when t=t0 show that when t=2t I=8/9I

##### Solution Summary

A circuit problem is solved by using integration of derivatives. The substitution to reduce the equations of a function are provided.

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