00:01
In this question, we are given this differential equation, the y -d -x is equal to y -square.
00:06
In part a, we want to find the general solution.
00:10
So we're going to gather the y on one side and the x on the other side.
00:18
So putting an integration sign on both sides, you can see that on the left, we are left with this.
00:29
On the right, we can integrate.
00:31
We will be just x plus c, where c is a constant.
00:35
1 over y squared is y to power minus 2 so i integrate will be y the power at 1 divide by the new power so i have minus 1 over y equals to x plus c so my 1 over y is minus x plus c so my y is equal to minus 1 over x plus z so this is my general solution.
01:10
Now in part b, what is the singular solution that is not included in the general solution? so now we know that y can never be zero because of this.
01:23
So y equals to zero is the singular solution that is not included in the general solution.
01:31
Now in part c, we want to sketch the family of curve and determine the points that which this initial function, initial condition to this differential equation, has a unique solution...