How to solve the separable differential equation and to the initial condition: y(0)=1 ?
1 Answer
Get the
Explanation:
We will begin to solve this first-order separable differential equation by separating it (no surprise there).
If we add
Now divide by
Multiply by
Yay! We've separated the equation: we have
Let's start with the more complicated one of these:
First, take out a
Now we can apply the substitution
In order to apply the substitution, we need to multiply the inside of the integral by
We can go ahead and substitute now:
Noticing that this is equivalent to
Since
As for the other integral,
Alright, we've solved our integrals so we now have:
Doing a little algebra to solve for
Note: Remember that manipulating the integration constant
Now we apply the initial condition
Therefore our solution is