Let y=y(x) be the solution of the differential equation (x^2+4 )^2 d y+ (2 x^3 y+8 x y-2 ) d x=0 . If y(0)=0 , then y(2) is equal to

Step-by-step solution

aligned & d y d x +y ( 2 x^3+8 x (x^2+4 )^2 )= 2 (x^2+4 )^2 & d y d x +y ( 2 x x^2+4 )= 2 (x^2+4 )^2 & IF =e^ 2 x x^2+4 d x & IF =x^2+4 & y (x^2+4 )= 2 (x^2+4 )^2 (x^2+4 ) & y (x^2+4 )=2 d x x^2+2^2 & y (x^2+4 )= 2 2 ⁻¹ ( x 2 )+c & 0=0+c=c=0 & y (x^2+4 )= ⁻¹ ( x 2 ) & y at x=2 & y(4+4)= ⁻¹(1) & y(2)= 32 aligned