compute the general solution (1-x)y'=y^2
Can anyone, solve this step by step?
Where did you get this problem? From a course in Calculus or Differential Equations? In either case you certainly should know how to integrate:
[tex](1- x)y'= (1- x)\dfrac{dy}{dx}= y^2[tex]
Can you integrate those?
One thing you can do is "flip" both sides:
becomes
(Notice the absolute value. ln(x) isn't defined for . If you know x< 1, for example, if you given a value for y(0)= 0, you can use just "1- x". On the other hand, if you have reason to believe x>1, say you are given a value of y(1), you need "x- 1".)