Matias Aguirre

Answered

2022-07-28

Show that the function defined in column I is a solution ofthe corresponding differential equation in Column II in everyinterval a1. $f(x)=x+3{e}^{-x}$

2. dy/dx+y=x+1

2. dy/dx+y=x+1

Answer & Explanation

kamphundg4

Expert

2022-07-29Added 20 answers

Given

$y=x+3{e}^{-x}$

$dy/dx=1-3{e}^{-x}$

Now for the second equation

dy/dx + y =

$(1-3{e}^{-x})+(x+3{e}^{-x})=$

= 1 + x

$y=x+3{e}^{-x}$

$dy/dx=1-3{e}^{-x}$

Now for the second equation

dy/dx + y =

$(1-3{e}^{-x})+(x+3{e}^{-x})=$

= 1 + x

Joanna Mueller

Expert

2022-07-30Added 5 answers

$\frac{dy}{dx}=1-3{e}^{-x}$

$\frac{dy}{dx}+y=1-3{e}^{-x}+x+3{e}^{-x}=x+1$

so $f(x)=x+3{e}^{-x}$ is the solution of dy/dx + y =x=1

$\frac{dy}{dx}+y=1-3{e}^{-x}+x+3{e}^{-x}=x+1$

so $f(x)=x+3{e}^{-x}$ is the solution of dy/dx + y =x=1

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