Question

solve the differential equation:
dy/ dx = (6x^2) / (y(1+x^2))

Answer 1

\[ydy=\frac{ 6x^2 }{ 1+x^2 }dx\]

Answer 2

\[\int\limits_{}^{}ydy = 6 \int\limits_{}^{}\frac{ (x^2 +1) -1 }{ 1+x^2 }\]

Answer 3

do you know how to get the answers in ln? the options are
1. y = lnI1+x^3L +c
2. y^2 = -4lnI1+x^3I +c
3. y^2 = 4 ln I 1+x^2I +k where k = 2c

Answer 4

\[\int\limits_{}^{} y dy = 6 \int\limits_{}^{} dx - \int\limits_{}^{}\frac{ 1 }{ 1+x^2 } dx\]

Answer 5

\[y^2 = x - tanx + c\]

Answer 6

actually i dont know how to solve it in ln, sorry !!

Answer 7

well what if you derive each answer ??