On solving ( d y d x = x-y+3 2 x-2 y+5 ), the solution obtained is (x=2(x-y)+ (t)+c ), find (t )

Step-by-step solution

Given differential equation, ( d y d x = x-y+3 2(x-y)+5 ) Let ( x-y=t 1- d y d x = d t d x ), so ( array ll & 1- d t d x = t+3 2 t+5 d t d x = 2 t+5-t-3 2 t+5 = t+2 2 t+5 & 2 t+5 t+2 d t= d x & (2+ 1 t+2 ) d t=x+C^ & 2 t+ _e|t+2|=x+C^ & 2(x-y)+ |x-y+2|+C=x & 2(x-y)+ (t)+C=x (given) array ) On comparing, we get ( t=x-y+2 ) Hence, option (a) is correct.