Differential Equation dy/dx + yf'(x) = f(x).f'(x)

  • Thread starter zorro
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  • #1
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Homework Statement



Solve dy/dx + yf'(x) = f(x).f'(x) where f(x) is a given function of x.


The Attempt at a Solution



This is a linear differential equation where I.F. = e^f(x)
On solving, I got the answer as
y = f(x) - 1 which doesnot make sense as differentiating it doesnot give back the equation in question. Where am I wrong?
 

Answers and Replies

  • #2
Dick
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y=f(x)-1 is a solution. Put it into your original ODE and show you get an identity. It's not the most general solution though. You should probably keep a constant of integration.
 
  • #3
tiny-tim
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Hi Abdul! :smile:
Solve dy/dx + yf'(x) = f(x).f'(x) where f(x) is a given function of x.

On solving, I got the answer as
y = f(x) - 1 which doesnot make sense as differentiating it doesnot give back the equation in question. Where am I wrong?
You're wrong about being wrong.

d(f(x) - 1)/dx + (f(x) - 1)f'(x) = f(x).f'(x)

(but you have left out the constant of integration :redface:)

EDIT: Dick beat me to it! :biggrin:
 
  • #4
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Exactly at 5:47 P.M.!!

Ahh I made a very silly mistake. Thanks to both for your help :smile:
 

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