I am having problem solving this problem. Kind of stuck. Help would be veryy appreciated.
the problem is :
The differential equation y' = x^2 - y^2 -1 has y = -x as one of its solutions find the another solution.
i used one of the solution and
i let y = u - x
therefore y' = u'-1
plug it back into the equation and i got
u'-1 = x^2 - ( u-x)^2 -1
u'-1 = x^2 - (u^2-2ux+x^2)-1
u'-1 = x^2 - u^2 + 2ux - x^2 -1
u' = -u^2+2ux
u' = u(-u+2x)
I dunno if i am doing it correctly or not... i am stuck at the integration part