The Wronskian of functions u = f + 3g and v = f - g can be derived from the known Wronskian of f and g, which is given as W(f, g) = tcos(t) - sin(t). To find W(u, v), the expression W(u, v) = (f + 3g)(f - g)' - (f + 3g)'(f - g) must be expanded. The derivatives involved are (f - g)' = f' - g' and (f + 3g)' = f' + 3g'. Utilizing properties of determinants can simplify the calculation of W(u, v) in terms of simpler Wronskians.
PREREQUISITESMathematics students, particularly those studying differential equations, and educators looking to deepen their understanding of Wronskian determinants and their applications in function analysis.
You have fg' - gf' = tcos(t)-sin(t).Success said:If the Wronskian of f and g is tcos(t)-sin(t), and if u=f+3g, v=f-g, find the Wronskian of u and v.
W=fg'-gf'
(f+3g)(f-g)'-(f+3g)'(f-g)
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