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

[zorro]

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?

 

[Dick]

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.

 

[tiny-tim]

Hi Abdul!

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 )

EDIT: Dick beat me to it!

 

[zorro]

Exactly at 5:47 P.M.!

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