Given the differential equation y" + 4 y' - 12y = 10x2 + 7 (1) Find the characteristic equation, (2) Solve the characteristic equation, and (3) equation. A y = C, x-6 + C,x2

Calculus: Early Transcendentals
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Author:James Stewart
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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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Given the differential equation
y" + 4 y' - 12y
10x2 + 7
%3!
(1) Find the characteristic equation, (2) Solve the characteristic equation, and (3) Write the general solution of the characteristic
equation.
Ac = C,x-6 + C, x2
-6x
B Yc = C,e- +
3/5
cos
3/5
sin
10
10
2.275x
+
C, e-5.275x
= C
70
70
E) y. = C, cos
10
+ C, sin
10
1.772x
-6.772x
'c = C,
+ C,e
F
Transcribed Image Text:Given the differential equation y" + 4 y' - 12y 10x2 + 7 %3! (1) Find the characteristic equation, (2) Solve the characteristic equation, and (3) Write the general solution of the characteristic equation. Ac = C,x-6 + C, x2 -6x B Yc = C,e- + 3/5 cos 3/5 sin 10 10 2.275x + C, e-5.275x = C 70 70 E) y. = C, cos 10 + C, sin 10 1.772x -6.772x 'c = C, + C,e F
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