Reference no: EM133029181
MATH 381 - Differential Equations Assignment - University of Regina, Canada
Q1. Solve the given differential equations.
a. 9x2y'' + 9xy' + (9x2 - 7)y = 0
b. 4x2y'' + 4xy' + (16x2 - 36)y = 0
c. x2y'' + 4xy' + 4x2y = 0 using the substitution y = x-3/2u(x).
Q2. Show that y = x½ w(x2) is a solution of the differential equation y'' + 4x2y = 0, x > 0, whenever w is a solution of Bessel's equation of order ¼, that is t2w'' + tw' + (t2 - 1/16)w = 0, t > 0.
Q3. Verify that the vector X is a solution of the given linear system.
Q4. Determine whether the given vectors form a fundamental set on the interval (-∞, ∞).
Q5. Find the general solution of the given system.
Q6. Find the general solution of the given system.
dx/dt = 2x - 2y - 2z
dy/dt = -x + 2y
dz/dt = -x + 2z
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