Let the solution of the equation d y d x =y+ ₀^2 y d x is y(x) . If y(0)=1 , then find the absolute value of [y(2)] . [Note: [k] denotes greatest integer function less than or equal to k .]

Step-by-step solution

Let aligned A & = ₀^2 y d x d y y+A & =d x aligned Its solution is (y+A)=x+c Given aligned y(0) & =1, so c= (1+A) Y & =(1+A) e^x-A A & = ₀^2 y d x= ₀^2 ((1+A) e^x-A ) d x= e^2-1 4-e^2 aligned Hence solution is y(x)= 3 e^x-e^2+1 4-e^2