The equation of the curve passing through the point (-1,-2) which satisfies ` (dy)/(dx) =-x^(2) -1/(x^(3))` is

Options

A. ` 17x^(2)y-6x^(2) +3x^(5) -2=0`
B. `6x^(2)y +17 x^(2) +2x^(5) -3=0`
C. `6xy -2x^(2) +17x^(5) =3=0`
D. ` 17x^(2)y +6xy -3x^(5) +5=0`

Answer

B

Explanation

` (dy)/(dx) -x^(2) -1/(x^(3))`
` Rightarrow int dy = int (-x^(2) -1/x^(3))dx`
` Rightarrow y = x^(3)/3 + 1/(2x^(2))+c`
Putting (-1,-2) we, get
` -2 = 1/3 +1/2 +c Rightarrow C= - 17/6`
` Rightarrow 6x^(2)y = 2x^(5) +3 -17x^(2)`
` Rightarrow 6x^(2)y +17 x^(2)+2x^(5)-3=0`