Most Important Selected Qs for JEE AdvancedMathematicsDifferential Equations
If 1-x^6 + 1-y^6 =a (x^3-y^3 ) and d y d x =f(x, y) 1-y^6 1-x^6 then,
Options
- Af(x, y)= y x
- Bf(x, y)= x^2 y^2
- Cf(x, y)= 2 y^2 x^2
- Df(x, y)= y^2 x^2
Correct answer
B. f(x, y)= x^2 y^2
Step-by-step solution
aligned & - x^5 1-x^6 - y^5 1-y^6 d y d x =a (x^2-y^2 d y d x ) & (a y^2- y^5 1-y^6 ) d y d x =a x^2+ x^5 1-x^6 aligned d y d x = 1-y^6 1-x^6 x^2 (a 1-x^6 +x^3 ) y^2 (a 1-y^6 -y^3 ) ....(i) Also, (1-x^6 )- (1-y^6 ) 1-x^6 - 1-y^6 =a (x^3-y^3 ) or x^3+y^3=a ( 1-y^6 - 1-x^6 ) a 1-y^6 -y^3=a 1-x^6 +x^3 Hence, from equation (1), d y d x = 1-y^6 1-x^6 x^2 y^2