If solution of equation d y d x =y+ ₀^2 y d x , is y(x) . Then [ y(2) | is equal to (where [.] greatest integer function) ( given y(0)=1)

Step-by-step solution

d y d x =y+ ₀^2 y d x Say ₀^2 y d x=A d y d x =y+A d y y+A =d x (y+A)=x+B Given y(0)=1 B= (1+A) (y+A) (1+A) =x y+A=(1+A) e^x Now find ' A ' A= ₀^2 [(1+A) e^x-A , d x A= e^2-1 4-e^2 . . Hence solution y ( x )= (1+ e ^2-1 4- e ^2 ) e ^ x - ( e ^2-1 4- e ^2 )= 3 e ^ x - e ^2+1 4- e ^2 aligned & y(2)= 2 e^2+1 4-e^2 & |y(2) |=4 aligned