The order of the differential equation whose general solution is given by y = ( C ₁+ C ₂ ) ( x + C ₃ )- C ₄ e ^ x+ C ₅ is (where C ₁, C ₂, C ₃, C ₄, C ₅ are arbitrary constants)

Step-by-step solution

The order of a differential equation corresponds to the number of independent arbitrary constants in its general solution. The given general solution is y = (C₁ + C₂) (x + C₃) - C₄ e^ x + C₅ . The sum C₁ + C₂ reduces to a single arbitrary constant A . The exponential term -C₄ e^ x + C₅ simplifies to B e^x , where B = -C₄ e^ C₅ represents another independent constant. The phase shift C₃ remains as the third independent constant. The simplified form becomes y = A (x + C₃) + B e^x , containing three independent arbitr