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