If y=y(x) is the solution of the differential equation, 4-x^2 ~d y ~d x = ( ( ⁻¹ ( x 2 ) )^2-y ) ⁻¹ ( x 2 ),-2 x 2, y(2)= ^2-8 4 , then y^2(0) is equal to

Step-by-step solution

aligned & d y d x + ( ⁻¹ x 2 ) 4-x^2 y= ( ⁻³ x 2 )^3 4-x^2 & y e^ ( ⁻¹ x 2 )^2 2 = ( ⁻³ x 2 )^3 4-x^2 e^ ( ⁻¹ x 2 )^2 2 d x & y= ( ⁻¹ x 2 )^2-2+c e^ - ( ⁻¹ x 2 )^2 2 & y(2)= ^2 4 -2 c=0 & y(0)=-2 aligned