When you have 2 functions, y1=f(x) and y2=g(x), what are the rules for determing if they are linearly independent? If W(f(x), g(x))≠0 for some x in the interval, then f(x) and g(x) are linearly independent on the interval All of the above None of the above Cannot be determined

If W(f(x), g(x))≠0 for some x in the interval, then f(x) and g(x) are linearly independent on the interval

2 functions are said to be lineearly dependent on an interval I if what is true? None of the above If there exists two constants k1 and k2, both not zero, that satisfy the equation for all x's in interval Or, if there exists 2 numbers, c1 and c2, that make the wronskian zero than the function is linearly dependent All of the above Cannot be determined

If there exists two constants k1 and k2, both not zero, that satisfy the equation for all x's in interval Or, if there exists 2 numbers, c1 and c2, that make the wronskian zero than the function is linearly dependent

2 functions are said to be linearly independent on an interval I if what is true? None of the above The only solution to the equation is k1=k2=0 If the Wronskian is nonzero for some value x in the inveral, the functions are linearly independent All of the above Cannot be determined

The only solution to the equation is k1=k2=0 If the Wronskian is nonzero for some value x in the inveral, the functions are linearly independent

Wronskian definition All of the above None of the above y1 y2 y1' y2' y1y2'-y2y1' is called the wronskian of y1 and y2 Cannot be determined

y1 y2 y1' y2' y1y2'-y2y1' is called the wronskian of y1 and y2

Wronskian Test for Linear Independence: y''+P(x)y'+q(x)y=0 y1 and y2 are linearly independent W(y1,y2)≠0 for all x in (a,b) W(y1,y2)≠0 for at least one x0 in (a,b) Cannot be determined All of the above None of the above

y1 and y2 are linearly independent W(y1,y2)≠0 for all x in (a,b) W(y1,y2)≠0 for at least one x0 in (a,b)

2nd Order Linear ODE's real roots for b^2>4AC None of the above y1=e^r1x, y2=e^r2x factor the equation Cannot be determined All of the above

y1=e^r1x, y2=e^r2x factor the equation

2nd Order Linear ODE's real roots for b^2=4AC None of the above All of the above y1=e^r1x, y2=xe^r1x. Factor equation and if factors are perfect square remember to put x in front of y2 Cannot be determined

y1=e^r1x, y2=xe^r1x. Factor equation and if factors are perfect square remember to put x in front of y2

Wronskian & Linear Independence Flashcards

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Calculus - Geometry

user_hodr Created by 6 mon ago

Cards in this deck(7)

When you have 2 functions, y1=f(x) and y2=g(x), what are the rules for determing if they are linearly independent?

2 functions are said to be lineearly dependent on an interval I if what is true?

2 functions are said to be linearly independent on an interval I if what is true?

Wronskian definition

Wronskian Test for Linear Independence: y''+P(x)y'+q(x)y=0

2nd Order Linear ODE's real roots for b^2>4AC

2nd Order Linear ODE's real roots for b^2=4AC

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Wronskian & Linear Independence Flashcards

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