Question

The set of linearly independent solutions of the differential equation $(D^4 - D^3)y = 0; D = \frac{d}{dx}$ is

• A. $\{1, x, e^{-x}, x e^{-x}\}$
• B. $\{1, x, x^2, e^{-x}\}$
• C. $\{1, x, e^x, x e^x\}$
• D. $\{1, x, x^2, e^x\}$

Hint:

For repeated root $m = 0$ with multiplicity 3, the solutions are polynomials $1, x, x^2$ up to degree $3-1 = 2$. Combined with $e^x$, we get $\{1, x, x^2, e^x\}$.

Answer 1

The Correct Option is D