Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202526 Apr 2025Morning ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation dy d x = x y is

Options

  1. Ax= c cosec y , where c is the constant of integration.
  2. Bx= c~sec~ y , where c is the constant of integration.
  3. Cx=x y , where c is the constant of integration.
  4. Dx= c y , where c is the constant of integration.

Correct answer

B. x= c~sec~ y , where c is the constant of integration.

Step-by-step solution

The differential equation is dy dx = x y . Separating variables and writing y = 1/ y gives y dy = x dx . Integrating both sides yields | y| = | x| + |C| using standard antiderivatives d = | | and d = | | . Applying the logarithmic property a - b = a b produces | y x | = |C| . Exponentiating both sides results in y x = C . Substituting y = 1 y and rearranging leads to x y = 1 C , where 1 C is an arbitrary constant. The general solution x y = c corresponds exactly to option B .

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