## soumyan Group Title solve this ordinary differential equation dy/dx = 1-xy-y+x , given y(0),= 1. one year ago one year ago

1. zepdrix Group Title

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,$\large y'=(x+1)(1-y)$

2. zepdrix Group Title

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

3. soumyan Group Title

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...

4. zepdrix Group Title

cool c:

5. mathslover Group Title

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