Given that fx and gA are independent solutions of a linear h

Given that f(x) and g(A) are independent .solutions of a linear homogeneous differential equation on (a. b), which of the following must also be solutions? 0 (D) 2 f(x) - 3 g(x) f(x) g(x) f(x) g(x) Both (A) and (B) Both (B) and (C)

Solution

if f(x), g(x) are linearly independent solutions of a homogeneous differential equations then c₁ f(x) +c₂ g(x) is also a solution for all values of c₁ and c₂..

Hence, 0 is a solution of the given homogeneous differentail equation and 2 f(x) -3g(x) is also solution of the differential equation.

Answer (D).