Question

Given the initial value problem

Answer 1

did u even read your question before posting

Answer 2

Given the initial value problem \[(\cos t) x^{'} = (\sin t) x-\sqrt{t-1} , x (\alpha) = \beta \]

Answer 3

if \[\alpha=1.5, \beta=0\] find the interval so that the initial value problem (IVP) is guaranteed by Existance and uniqueness Theorem (EUT) to have unique solution by using three methods below

Answer 4

a)theorem 1.1(only for linear DE,existence and uniqueness theorem)
with \[a_{0} (t) = \cos t\] ,where \[a_{0}(t)\] is the coeficient of x'

b) theorem 1.1 with \[( a _{0}) =1 \] after modifying the DE

c)theorem 1.2 ( for linear and non linear DE)