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Use Cauchy’s Integral Formula to evaluate ∫
zdz
C Z2−3z+2
, where C is the
circle |z − 2| =
1
2
Evaluate the integral ∫ (z̅)
2dz 2+i
a) Along the line y =
x
2
b) Along the real axis from 0 to 2 and then vertically 0 to 2+i
Consider an electric circuit with an inductance of 0.05 henry, a resistance of 20 ohms, a condenser of capacitance of 100 micro farads and an E = 100 volts. Find I and Q given the initial conditions Q = 0, I = 0 at t = 0
Write applications of Differential Equation in Physics
(D^2-2D+5)y=x+5
r+4s+t+rt-s²=0
Form the PDE of the following by eliminating arbitrary functions from:
1.xyz=(x^2+y^2-z&^2)
2 . z= (x+y)f(x^2-y^2)
Find the general solution of the equation:
𝑥^2𝑦" − 9𝑥𝑦′ + 25𝑦 = 0
Solve the initial value problem:
𝑥^2𝑦" + 𝑥𝑦′ + 9𝑦 = 0; 𝑦(1) = 2, 𝑦′(1) = 0
Find the general solution of the equation:
𝑥^2𝑦" − 7𝑥𝑦′ + 12𝑦 = 0
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#340153 on Dec 2023