Solving differential equations

  • #1
270
1
[SOLVED] Solving differential equations

Homework Statement



Find the solution:
dy/dx = (1+y^2)/(1+x^2)
hint: there is a formula tan(a + b) that will simplify your answer.
y(0)=1

Homework Equations





The Attempt at a Solution



I seperated the variables and integrated ending up with

arctan(y)=arctan(x)+c
I do not see how to take this to the answer below. I understand how to use the formula they gave me in the hint but I do not see how it applies here...

the answer is
y=(1+x)/(1-x) this problem is from my exam review we have the solutions but not how to get them...
 

Answers and Replies

  • #2
exk
119
0
tan(arctan(y))=y

take the tangent of both sides and then the formula for tan(a+b) goes to work since you have tan(arctan(x)+c), which is also (tan(a)+tan(b))/(1-tan(a)tan(b)) so you get (x+tan(c))/(1-x*tan(c)).

y(0)=1 --> tan(c)=1 --> c= arctan(1)

and you get

y=(x+tan(c))/(1-x*tan(c)) --> (x+1)/(1-x)
 
  • #3
270
1
thanks a lot I was thinking you had to take the tan of both sides but I wasn't sure you cleared it up nicely.
 

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