(6) (a) For each of the following differential equatons: • Determine the order of the differential equation. • Classify the differential equation as linear or nonlinear. • If the differential equation is linear, classify it as homogeneous or inhomogeneous. d?q (i) L + R+ ta = V, where L, R, C, and V are non-zero constants. dt2 dt 2 d?s (ii) m- dt2 ds' = K, where m, y, and K are non-zero constants. Explain how you identify each feature.

Calculus: Early Transcendentals
8th Edition
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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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(6) (a) For each of the following differential equatons:
• Determine the order of the differential equation.
• Classify the differential equation as linear or nonlinear.
• If the differential equation is linear, classify it as homogeneous or inhomogeneous.
d?q
(i) L-
dq
+ ta = V, where L, R, C, and V are non-zero constants.
+ R-
dt2
d?s
dt
(當)
ds
= K, where m, Y, and K are non-zero constants.
dt?
dt
Explain how you identify each feature.
(b) Solve the following initial value problem:
dy
sint
y(0) = 2.
dt
cos? t
Transcribed Image Text:(6) (a) For each of the following differential equatons: • Determine the order of the differential equation. • Classify the differential equation as linear or nonlinear. • If the differential equation is linear, classify it as homogeneous or inhomogeneous. d?q (i) L- dq + ta = V, where L, R, C, and V are non-zero constants. + R- dt2 d?s dt (當) ds = K, where m, Y, and K are non-zero constants. dt? dt Explain how you identify each feature. (b) Solve the following initial value problem: dy sint y(0) = 2. dt cos? t
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