x-t-c-tx-t-c-is-constant-1-Find-x-t-2-Find-x-t-when-x-0-x-0-

Question Number 205172 by shunmisaki007 last updated on 12/Mar/24

x (t) = c + {t x}^{'} (t) ∣ c is constant .

(1) Find x (t) .

(2) Find x (t) when x (0) = x_{0} .

Commented by lepuissantcedricjunior last updated on 12/Mar/24

x (t) = c + {t x}^{'} (t) c \in R

o n a

{t x}^{'} (t) - x (t) = - c

x_{k} = e^{\int \frac{1}{t} d t} = {k e}^{l n t} = k t

f a i s o n s v a r i e r l a c o n s t a n c e k (t)

x (t) = k (t) t

x^{'} (t) = k^{'} (t) t + k (t)

{t x}^{'} (t) - x (t) = - c

t^{2} k^{'} (t) + k (t) t - k (t) t = - c

k^{'} (t) = - \frac{c}{t^{2}} => k (t) = \frac{c}{t} + m o u m \in R

x_{m} (t) = m t + c

x (o) = x_{0}

=> x_{m} (0) = m (0) + c = x_{0}

=> c = x_{0}

x_{m} (t) = m t + x_{0} o u m \in R

x_{m} (t) = m t + x_{0} o u m \in R

\dots \dots \dots \dots . l e p u i s s a n t D r \dots \dots \dots \dots \dots \dots \dots .