# General solution of diffential equation

1. May 2, 2014

### delsoo

1. The problem statement, all variables and given/known data

i cant reduce the eq to y= (X+1)/(x+c ) , which part is wrong?

2. Relevant equations

3. The attempt at a solution

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2. May 2, 2014

### Staff: Mentor

$$y=\frac{c(1+x)}{1+c(1+x)}$$
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

3. May 2, 2014

### 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 ?

4. May 2, 2014

Of course.

Chet

5. May 2, 2014

### delsoo

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

6. May 3, 2014

### Staff: Mentor

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