Verify that the following functions are solutions to the given differential equa

Ernstfalld

Ernstfalld

Answered question

2021-10-24

Verify that the following functions are solutions to the given differential equation. y=2exx1 solves y=y+x

Answer & Explanation

cheekabooy

cheekabooy

Skilled2021-10-25Added 83 answers

y=2exx1  solves  y=y+x
y=2exx1 (1)
y=ddx(2exx1)
=2ex1+0 (exponential diff. and general power rule)
=(2exx1)+x (y  from(1)) (reforming)
=y+x (satisfying the differental equation)
Result
y=ddx(2exx1)=2ex1+0 (exponential diff. and general power rule)
=(2exx1)+x=y+x (satisfying the differental equation)

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