Fourier and differential equations. Found this problem, just so you know it's my first time using Fourier to solve differential equations. f′′(x)+f(x)=3 cos (2x)

Pranav Ward

Pranav Ward

Answered question

2022-09-11

Fourier and differential equations
Found this problem, just so you know it's my first time using Fourier to solve differential equations.
f ( x ) + f ( x ) = 3 cos ( 2 x )

Answer & Explanation

Everett Melton

Everett Melton

Beginner2022-09-12Added 12 answers

Step 1
F [ f ( x ) + f ( x ) ] = F [ 3 cos ( 2 x ) ]
or
( ( i ω ) 2 + 1 ) F ( ω ) = 3 π 2 δ ( w 2 ) + 3 π 2 δ ( w + 2 )
and then
F ( ω ) = 3 π 2 δ ( w 2 ) + 3 π 2 δ ( w + 2 ) ( ( i ω ) 2 + 1 )
Step 2
Finally
F 1 ( 3 π 2 δ ( w 2 ) + 3 π 2 δ ( w + 2 ) ( ( i ω ) 2 + 1 ) ) = cos ( 2 x )

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