So I'm in my first differential equations college class, and we just learned about separable equations. Now, I have no trouble solving these equations, but I'm having trouble understanding what is actually happening when we solve a separable equation.
For example, the generic separable differential equation is N(y)dy/dx=M(x).
Then you simply cancel out the dx and pop it on the right side resulting in two clean integrals. N(y)dy=M(x)dx which you can then solve easily.
Here's my problem. I don't understand how we can just split a derivative and algebraically separate dx from dy. I understand that we're not actually canceling out the dx, but I'm not sure what exactly is happening. Could somebody please elaborate?
Thank you!
For example, the generic separable differential equation is N(y)dy/dx=M(x).
Then you simply cancel out the dx and pop it on the right side resulting in two clean integrals. N(y)dy=M(x)dx which you can then solve easily.
Here's my problem. I don't understand how we can just split a derivative and algebraically separate dx from dy. I understand that we're not actually canceling out the dx, but I'm not sure what exactly is happening. Could somebody please elaborate?
Thank you!