Problem 3. The linear transformation T : C²(R) –→ C°(R) is defined by d d T(f) drzf +3-f – 4f. Show that the functions y1 (x) and y2() from Problem 1 and Problem 2 form a basis for kerT. (Hint: By Theorem 8.1.6, the set of solutions to a second order differential equation y" + 3y' – 4y = 0 is a vector space of dimension 2.)

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Linear Methods

Problem 3. The linear transformation T : C²(R) → C°(R) is defined by
d
T(f)
držf +3-f – 4f.
%3D
dr²"
dx
Show that the functions y1(x) and y2(r) from Problem 1 and Problem 2 form a basis for kerT.
(Hint: By Theorem 8.1.6, the set of solutions to a second order differential equation
y" + 3y' – 4y = 0
is a vector space of dimension 2.)
Transcribed Image Text:Problem 3. The linear transformation T : C²(R) → C°(R) is defined by d T(f) držf +3-f – 4f. %3D dr²" dx Show that the functions y1(x) and y2(r) from Problem 1 and Problem 2 form a basis for kerT. (Hint: By Theorem 8.1.6, the set of solutions to a second order differential equation y" + 3y' – 4y = 0 is a vector space of dimension 2.)
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