COMEDK20269 May 2026Morning ShiftMathematicsDifferential EquationsActual
The particular solution of the equation ( dy dx ) = a , where a R and y = 2 when x = 0 is
Options
- A( x y-2 ) = a
- B( x-2 y ) = a
- C( y-2 x ) = a
- D( y+2 x ) = a
Correct answer
C. ( y-2 x ) = a
Step-by-step solution
Given differential equation is ( dy dx ) = a dy dx = ⁻¹(a) Integrating both sides with respect to x : dy = ⁻¹(a) dx y = x ⁻¹(a) + C Substituting y = 2 when x = 0 : 2 = 0 + C C = 2 Substituting C = 2 in the general solution: y = x ⁻¹(a) + 2 y - 2 x = ⁻¹(a) ( y - 2 x ) = a Answer: ( y-2 x ) = a