# Initial Value Problem

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• February 9th 2010, 09:34 AM
JQ2009
Initial Value Problem
I have a number of equations where I have to solve the initial value problem. I don't really understand what my notes say and the examples they give seem to basic to the ones I have to do.

Could someone please help understand how to go about doing the following?

arcsint = x^4(1-t^2)^1/2 dx/dt, x(0) = 0
• February 9th 2010, 09:50 AM
Jester
Quote:

Originally Posted by JQ2009
I have a number of equations where I have to solve the initial value problem. I don't really understand what my notes say and the examples they give seem to basic to the ones I have to do.

Could someone please help understand how to go about doing the following?

arcsint = x^4(1-t^2)^1/2 dx/dt, x(0) = 0

Your DE is separable so

$
x^4\,dx = \frac{\sin^{-1} t}{\sqrt{1-t^2}}dt
$

Integrate both sides and then use your IC to determine the constant of integration.