Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK20269 May 2026Evening ShiftMathematicsDifferential EquationsActual

The particular solution of the differential equation (x - y)(dx + dy) = (dx - dy) when y = -1 and x = 0 is

Options

  1. A| x - y x + y | = 1
  2. B|x - y| = x - y + 1
  3. C|x + y| = x - y + 1
  4. D|x - y| = x + y + 1

Correct answer

D. |x - y| = x + y + 1

Step-by-step solution

Given differential equation is (x - y)(dx + dy) = dx - dy Let x - y = u and x + y = w Differentiating, we get dx - dy = du and dx + dy = dw Substituting these in the given equation: u dw = du du u = dw Integrating both sides: du u = dw |u| = w + C Substituting back u = x - y and w = x + y : |x - y| = x + y + C Given that y = -1 when x = 0 : |0 - (-1)| = 0 - 1 + C 1 = -1 + C C = 1 Therefore, the particular solution is: |x - y| = x + y + 1 Answer: |x - y| = x + y + 1

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 COMEDK PYQs