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Assignment -
Q1. Solve the given equations.
a) Given ty'' + (t - 1)y' - y = 0, t > 1
b) Given y'' + xy = 0; y(0) = 1; y'(0) = 0
c) Given y''' - 6y'' + 11y' - 6y = 0
d) Given F = (3y - z)i + (x + 3z)j + (3x - y)k
Q2. Is the integral ∫A · dr path independent if A = (2x - y)i + (x + y)j?
Q3. Evaluate around a unit circle centered at the origin. What is the value of the integral if we take a clockwise direction?
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