# Answer to Question #28171 in Differential Equations for Debrah

Question #28171

Given the Initial Value Problem (cos t)x' = (sin t)x - (t-1)^(1/2) , x(m) = n

i) If m = 1.5, n = 0, find the interval so that the Initial Value Problem (IVP) ia guaranteed by the Existence and Uniqueness Theorem (EUT) to have a solutionnby using the three methods :

a) Linear Case, with Ao(t) = cos t, where Ao (t) is the coefficient of x'

b) Linear Case, with Ao(t) = 1 after modifying the Differential Equation

c) General Case

Compare the answers you obtained in a), b) and c)

ii) Repeat i) with m = 8(pi) n = N

i) If m = 1.5, n = 0, find the interval so that the Initial Value Problem (IVP) ia guaranteed by the Existence and Uniqueness Theorem (EUT) to have a solutionnby using the three methods :

a) Linear Case, with Ao(t) = cos t, where Ao (t) is the coefficient of x'

b) Linear Case, with Ao(t) = 1 after modifying the Differential Equation

c) General Case

Compare the answers you obtained in a), b) and c)

ii) Repeat i) with m = 8(pi) n = N

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