General solution of differential equation

[delsoo]

Homework Statement

i can't reduce the eq to y= (X+1)/(x+c ) , which part is wrong?

Homework Equations

The Attempt at a Solution

 

[Chestermiller]

You already have it.
$$y=\frac{c(1+x)}{1+c(1+x)}$$
Divide numerator and denominator by c:
$$y=\frac{(1+x)}{(1+1/c)+x}$$
Let C = 1 + 1/c
$$y=\frac{(1+x)}{C+x}$$
Chet

 

[delsoo]

can we straight sub C =1 + 1/c ? the c is the question not the original c (constant ) from the integrate( (dx/X+1)) ? dx ?

 

[Chestermiller]

can we straight sub C =1 + 1/c ? the c is the question not the original c (constant ) from the integrate( (dx/X+1)) ? dx ?

Of course.

Chet

 

[delsoo]

the c is the question the original c (constant ) from the integral ( (dx/X+1)) ? dx ? am i right?

 

[Chestermiller]

the c is the question the original c (constant ) from the integral ( (dx/X+1)) ? dx ? am i right?

In your original solution, the choice of adding ln c as the constant of integration was not unique. You could just as easily have added a different constant, say c' (i.e., without the natural log), without affecting the correctness of the solution.

Chet