Question

solve this ordinary differential equation
dy/dx = 1-xy-y+x , given y(0),= 1.

Answer 1

Hmm so it looks like this is separable.
Just takes a little bit of work on the right side.
Factor by grouping.

\[\large y'=1-xy-y+x\]Factoring a -y out of each of the middle terms gives us,\[\large y'=1-y(x+1)+x\]We'll rewrite it like this,\[\large y'=(x+1)-y(x+1)\]Now we can factor an x+1 out of each term, giving us,\[\large y'=(x+1)(1-y)\]

Answer 2

Separating variables gives us,\[\large \frac{dy}{1-y}=(x+1)dx\]
Understand how to solve it from here? :o

Answer 3

thanks for solution..... i done this method in my exam and today or by tomorrow i wil get my result... i wanted to confirm.... thank u so much...

Answer 4

cool c:

Answer 5

And also @soumyan : \[\large{\color{orange}{\textbf{WELCOME TO OPENSTUDY}}}\]