Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202012 Oct 2020Evening ShiftMathematicsDifferential EquationsActual

The differential equation obtained by eliminating the arbitrary constants from the equation y²=(2 x+c)⁵ is

Options

  1. A( d y d x )⁴-625 y⁴=0
  2. B( d y d x )⁵-3125 y³=0
  3. C( d y d x )³-125 y³=0
  4. Dx y d y d x =5

Correct answer

B. ( d y d x )⁵-3125 y³=0

Step-by-step solution

We have y²=(2 x+c)⁵ ...(i) 2 y dy dx =5(2 x + c )⁴(2) y dy dx =5(2 x + c )⁴ (2 x+c)= [ y 5 ( d y d x ) ]^ 1 4 and substituting value of (2 x+c) in eq. (i), we write y²= [ y 5 ( d y d x ) ]^ 5 4 Raising both sides to power of 4 , we get aligned & y⁸= [ y 5 ( d y d x ) ]⁵= y⁵ 3125 ( d y d x )⁵ & 3125 y³= ( d y d x )⁵ aligned

Practice Differential Equations on Quantrex Academy →

More from Differential Equations

The general solution of the differential equation (x y x ) d y= (y y x -x ) d x is 2025The general solution of the differential equation (x+y) d y=d x is 2025If Ax ^3+ Bxy =4 (A and B are arbitrary constants) is the general solution of the differential equation F(x) d^2 y d x^2 +G(x) d y d x -2 y=0 , then F(1)+G(1)= 2025If y=A t^2+ B t (A,B are parameters) is general solution of the differential equation f(t) y^ (t)+g(t) y^ (t)+h(t) y=0 then 2 f(t)+t^2 h(t)= 2025The general solution of the differential equation (2 x-y)^2 d y-2(2 x-y)^2 d x-2 d x=0 is 2025The general solution of the differential equation x x d y=(x x-y) d x is 2025If a and b are arbitrary constants, then the differential equation corresponding to the family of curves y= (a x+b) is 2025The general solution of the differential equation x y(y+2) d y+ (y^3-1 ) d x=0 is 2025 Full Differential Equations list All MHT CET PYQs