1st order separable diff eq... integration problem

[hardyaa1]

The problem is written as:

y^2 * sqrt(1-x^2) * dy = arcsin(x) dx ; y(0)=1

I know that d/dx(arcsin x) = 1 / (1-x^2)^1/2 ... which means if i go with separation of variables,
the right side will be the integral of arcsin (x) / (1-x^2)^1/2 however, i don't really know how to
integrate that.

This question SHOULD be pretty simple, the class just started. Maybe i'm missing something

 

[Deleted member 4993]

The problem is written as:

y^2 * sqrt(1-x^2) * dy = arcsin(x) dx ; y(0)=1

I know that d/dx(arcsin x) = 1 / (1-x^2)^1/2 ... which means if i go with separation of variables,
the right side will be the integral of arcsin (x) / (1-x^2)^1/2 however, i don't really know how to
integrate that.

This question SHOULD be pretty simple, the class just started. Maybe i'm missing something

After separating variables

substitute:

u = arcsin(x)

Now solve...

 

[tkhunny]

You fell asleep in class some semesters ago when you were studying Substitution or Derivatives of Inverse Trig Functions - maybe both.

Answer this: \(\displaystyle \frac{d}{dx}arcsin(x)\;=\;??\)

Now think about substitution.

 

[hardyaa1]

THANKS so much.

my math really is rusty, I spent a while yesterday trying to use integration-by-parts and I suppose I forgot that the substitution method existed... wow the rest of this class should be fun :shock: