Solve the differential equation\({\rm{\;}}\frac{{2{\rm{dy}}}}{{{\rm{dx}}}} - {\rm{y}}\sec {\rm{x}} = {{\rm{y}}^{3{\rm{\;}}}}\tan {\rm{x}}\)
1
\(\frac{{\sec {\rm{x}} + \tan {\rm{x}}}}{{{{\rm{y}}^2}}} = \left( {\sec {\rm{x}} + \tan {\rm{x}}} \right) + {\rm{x}} + {\rm{c}}\)
2
\(\frac{{\sec {\rm{x}} + \tan {\rm{x}}}}{{{{\rm{y}}^2}}} = - \left( {\sec {\rm{x}} + \tan {\rm{x}}} \right) + {\rm{x}} + {\rm{c}}\)
3
\(\frac{{\sec {\rm{x}} + \tan {\rm{x}}}}{{{{\rm{y}}^2}}} = - \left( {\sec {\rm{x}} + \tan {\rm{x}}} \right) - {\rm{x}} + {\rm{c}}\)
4
\(\frac{{\left( {\sec {\rm{x}} + \tan {\rm{x}}} \right)}}{{{{\rm{y}}^3}}} = \left( {\sec {\rm{x}} + \tan {\rm{x}}} \right) + {\rm{x}} + {\rm{c}}\)