dy dt - e2y cosht+e2 sinh t cosht + ey cosh t (a) Factorise the numerator and denominator of the right-hand side of the differential equation, and hence write it in the form dy dt = f(t)g(y). (b) Hence find the general solution in implicit form of the differential equation. (c) Find the particular solution in implicit form of the differential equation that satisfies the initial condition y = 0 when t = 0.
dy dt - e2y cosht+e2 sinh t cosht + ey cosh t (a) Factorise the numerator and denominator of the right-hand side of the differential equation, and hence write it in the form dy dt = f(t)g(y). (b) Hence find the general solution in implicit form of the differential equation. (c) Find the particular solution in implicit form of the differential equation that satisfies the initial condition y = 0 when t = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:This question concerns the differential equation
dy e2 cosht+e2 sinh t
dt
cosht + ey cosh t
-
(a) Factorise the numerator and denominator of the right-hand side of
the differential equation, and hence write it in the form
dy
dt
= f(t)g(y).
(b) Hence find the general solution in implicit form of the differential
equation.
(c) Find the particular solution in implicit form of the differential
equation that satisfies the initial condition y
= 0 when t = 0.
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