Hi all,
still new to differential equations, so forgive my ignorance.
suppose we have an equation:
x(dy/dx) = y^2 - y
Very straightforward to solve.
Solved for ln|xy/(y-1)| = C
However the question asked for the solution which intersects the points (0,1) and then a second solution which intersects (0,0).
I can solve this second part by doing e^ of both sides and throwing the ol algebra hat on however I am concerned because at one point in my solution, x and y could not be 0, and then because of manipulation, they suddenly could be. This had alarm bells going off left right and center and I do not understand how they can not be a solution and then suddenly are because of manipulation.
If I did do something wrong I apologize and would love some insight in this.
thanks in advance
edit: and for the sake of my weigh in, I would probably answer that there is no solution at those points.
still new to differential equations, so forgive my ignorance.
suppose we have an equation:
x(dy/dx) = y^2 - y
Very straightforward to solve.
Solved for ln|xy/(y-1)| = C
However the question asked for the solution which intersects the points (0,1) and then a second solution which intersects (0,0).
I can solve this second part by doing e^ of both sides and throwing the ol algebra hat on however I am concerned because at one point in my solution, x and y could not be 0, and then because of manipulation, they suddenly could be. This had alarm bells going off left right and center and I do not understand how they can not be a solution and then suddenly are because of manipulation.
If I did do something wrong I apologize and would love some insight in this.
thanks in advance
edit: and for the sake of my weigh in, I would probably answer that there is no solution at those points.
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