MHT CET202314 May 2023Evening ShiftMathematicsDifferential EquationsActual
The differential equation representing the family of curves y^2=2 c (x+ c ) , where c is a positive parameter, is of
Options
- Aorder 1, degree 4
- Border 2, degree 3
- Corder 2, degree 4
- Dorder 1, degree 3
Correct answer
D. order 1, degree 3
Step-by-step solution
y^2=2 c (x+ c )... (i) Differentiating w.r.t. x , we get 2 y d y ~d x =2 c ... (ii) Substituting (ii) in (i), we get aligned & y^2=2 y d y ~d x (x+ y d y ~d x ) & y=2 x d y ~d x +2 d y ~d x y d y ~d x & (y-2 x d y ~d x )^2=4 y ( d y ~d x )^3 aligned This is a differential equation of order 1 and degree 3 .