The particular solution of differential equation e ^ d y d x =(x+1), y(0)=3 is

Step-by-step solution

aligned & e ^ d d x =(x+1) & d y ~d x = (x+1) aligned Integrating on both sides, we get aligned d y & = (x+1) d x+ c y & =x (x+1)- x x+1 ~d x+ c & =x (x+1)- x+1-1 x+1 ~d x+ c & =x (x+1)- (1- 1 x+1 ) d x+ c y & =x (x+1)-x+ (x+1)+ c . aligned Since y(0)=3 , i.e., y=3 when x=0 aligned & 3=0+ c c =3 & y=x (x+1)+ (x+1)-x+3 & y=(x+1) (x+1)-x+3 aligned