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Separable Equations Problems?

  • Thread starter Chandasouk
  • Start date
  • #1
165
0
I have solutions for 2 problems but they are different from the ones my book provides. This may be due to some simplification they chose to do, but I am uncertain.

1) dy/dx = x2/y

ydy = x2dx

Integrate both sides and you get

y2/2 = x3/3 + C

My book gave 3y2 - 2x3 = C

2) dy/dx = x2 / y(1+x3)

y(1+x3)dy = x2dx

ydy = x2/(1+x3) dx

Integrating both sides, I got

y2/2 = 1/3*ln(1+x3) + C

but my book gave

3y2-2ln(1+x3) = C

Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
C is arbitrary. It could be anything. 6*C is also arbitrary. You may as well just label 6*C as C. Multiply both of your answers by 6. If C is arbitrary then e^C, 6C, C-1, etc etc are also arbitrary. Just call them C.
 
  • #3
165
0
Oh, I see. So my answers were correct. It seems my book likes not having fractions. Thanks again.
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
Oh, I see. So my answers were correct. It seems my book likes not having fractions. Thanks again.
Right, there's not single right expression. The answer keys will usually pick the simplest form of the constant. You should try and do that too.
 

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