In Problems 21–24, give the order (first, second, third, etc.) of each differential equation, where y represents a function of the variable x . 26. Is y = 8 x + 8 a solution of the differential equation d y d x = y x + 1 ? Explain.
In Problems 21–24, give the order (first, second, third, etc.) of each differential equation, where y represents a function of the variable x . 26. Is y = 8 x + 8 a solution of the differential equation d y d x = y x + 1 ? Explain.
Solution Summary: The author explains that the function y=8x+8 is a solution of the differential equation.
Evaluate the line integral
sin z dz,
So sin
where C is the portion of the curve y = x² from 0 to −1 + i.
Let f(z) be complex differentiable everywhere in C. Fix two distinct
complex numbers a and b and a circle C of radius R with |a| < R,|b| < R traversed in the
counter-clockwise direction. Evaluate the integral
Sc −
f(z)dz
(z - a)(z – b)
in terms of a,
b and the values of f at those points.
| Let C be a circle (with a positive radius) such that z = 1 lies in its interior.
Evaluate the contour integral
So Tz
zez
(z - 1)³
=
where C is traversed in the clockwise direction.
dz
Chapter 5 Solutions
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