BITSAT2014MathematicsDifferential EquationsActual
Solution of differential equation x²=1+ ( x y )⁻¹ d y d x + ( x y )⁻² ( d y d x )² 2 ! + ( x y )⁻³ ( d y d x )³ 3 ! + is
Options
- Ay²=x² ( x²-1 )+C
- By=x²( x-1)+C
- Cy²=x( x-1)+ C
- Dy=x² e^ x² + C
Correct answer
A. y²=x² ( x²-1 )+C
Step-by-step solution
x²=e^ ( x y )⁻¹ ( d y d x ) x²=e^ ( y x ) ( d y d x ) x²= y x d y d x or x x² d x= y d y Put x²=t 2 x d x=d t 1 2 t d t= y² 2 C+t t-t=y² or y²=x² ( x²-1 )+C