- #1
Saracen Rue
- 150
- 10
Homework Statement
If ##a>0## and ##b≠0##, solve the following stating the maximal domain for which the solution is valid:
##\sqrt{a^2-x^2}\cdot \frac{dy}{dx}+b=0,\ y\left(0\right)=0##
Homework Equations
[/B]
##\int _{ }^{ }\frac{1}{\sqrt{a^2-x^2}}dx=\arcsin \left(\frac{x}{a}\right)+c,\ a>0##
##\int _{ }^{ }\frac{-1}{\sqrt{a^2-x^2}}dx=\arccos \left(\frac{x}{a}\right)+c,\ a>0##
The Attempt at a Solution
I have no problems doing the actual integration and arrive at the correct solution of ##y=-b\arcsin \left(\frac{x}{a}\right),\ \left|x\right|<a\ ##. However, I also get ##y=b\arccos \left(\frac{x}{a}\right)-b,\ \left|x\right|<a\ ## as being a valid solution, whereas both the answers and my calculator don't include this solution. Is there a reason as to why this second answer would be omitted?