If y=y(x) is the solution of the differential equation d y ~d x +2 y= (2 x), y(0)= 3 4 , then y ( 8 ) is equal to:

Step-by-step solution

aligned & d y d x +2 y= 2 x, y(0)= 3 4 & I.F =e^ 2 d x =e^ 2 x & y e^ 2 x = e^ 2 x 2 x d x & y e^ 2 x = e^ 2 x (2 2 x-2 2 x) 4+4 +C & x=0, y= 3 4 3 4 1= 1(0-2) 8 +C & 3 4 =- 1 4 +C & 1=C & y= 2 2 x-2 2 x 8 +1 e^ -2 x & x= 8 , y= 1 8 (2 4 -2 4 )+e^ -2 ( 8 ) & y=0+e^ - 4 aligned