that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d²y dx² y = c₁e³x + ₂x³x y = = = -6y +9y=0; dx C₁e³x + Cate3x in terms of x, dy 6 +9y = dx = - Czxe3x) +9(c₁e³x +

Calculus: Early Transcendentals
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
d²y dy
+ 9y = 0;
dx² dx
When y = c₁e³x + ₂xe³x,
5/55/17
d²y
=
Thus, in terms of x,
dy
dx
dx²
=
+ 9y =
=
y = C1e3X + C,Xe3x
+ 9(C₁e³x + ₂x³x)
Transcribed Image Text:Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d²y dy + 9y = 0; dx² dx When y = c₁e³x + ₂xe³x, 5/55/17 d²y = Thus, in terms of x, dy dx dx² = + 9y = = y = C1e3X + C,Xe3x + 9(C₁e³x + ₂x³x)
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