state gov RPSC 2nd Grade Senior Teacher Mock Test Series 2025 Engineering Mathematics Differential Equations Non Exact Differential Equations
The solutions of Differential equation \(\left( {x{y^2}-{{\rm{e}}^{\frac{1}{{{{\rm{x}}^3}}}}}} \right)dx - {x^2}y\;dy = 0\) is
1
\(3{\rm{\;}}{{\rm{e}}^{\frac{1}{{{{\rm{x}}^3}}}}} + 2{\rm{\;}}{{\rm{x}}^2}{{\rm{y}}^2} = {\rm{C}}\)
2
\(3{\rm{\;}}{{\rm{e}}^{\frac{1}{{{{\rm{x}}^3}}}}}-2{\rm{\;}}{{\rm{x}}^{-2}}{{\rm{y}}^2} = {\rm{C}}\)
3
\(2{\rm{\;}}{{\rm{e}}^{\frac{1}{{{{\rm{x}}^3}}}}}-3{\rm{\;}}{{\rm{x}}^{-2}}{{\rm{y}}^2} = {\rm{C}}\)
4
\(\frac{1}{3}{{\rm{e}}^{\frac{1}{{{{\rm{x}}^3}}}}}{\rm{\;}}-{\rm{\;}}{{\rm{y}}^2}{{\rm{x}}^{-2}}{\rm{\;}} = {\rm{\;C}}\)
5
Question Not Attempted