Find the solution of the given initial value problem. y'-2y=e^(2t), y(0)=2

anudoneddbv 2022-07-30 Answered
Find the solution of the given initial value problem.
y 2 y = e 2 t , y ( 0 ) = 2
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Answers (1)

Killaninl2
Answered 2022-07-31 Author has 20 answers
Given equation is y 1 2 y = e 2 t
This is a linear equation of first order in y
where P(t)=-2 and Q ( t ) = e 2 t
P ( t ) d t = 2 1 d t = 2 t
Integrating Factor = e P ( t ) d t = e 2 t
Multiplying (1) with e 2 t , we get
e 2 t y 1 2 e 2 t y = 1 ( 2 )
(2) can be written as
d d t [ y e 2 t ] d t = 1 d t
y e 2 t = t + C
y ( t ) = t e 2 t + C e 2 t
we know that y(0)=2
so 0 e 0 + C e 0 = 2 C = 2
Therefore the general solution of (1) is y = t + 2 e 2 t
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