Solve y(x)=e^x(1+int_0^x e^(−t) y(t)dt)

Gerardo Aguilar

Gerardo Aguilar

Answered question

2022-10-16

Solve
y ( x ) = e x ( 1 + 0 x e t y ( t ) d t )

Answer & Explanation

imperiablogyy

imperiablogyy

Beginner2022-10-17Added 13 answers

Your equation can be written as:
y ( x ) = e x + 0 x e x t y ( t ) d t = exp ( x ) + [ exp y ] ( x ) .
Then, if Y(s) is the Laplace transform of y(x), you get
Y ( s ) = 1 s 1 + Y ( s ) s 1 Y ( s ) = 1 s 2
which means y ( x ) = e 2 x

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