Question

The differential equation of the family of curves y = Ae^3x + Be^5x, where A and B are arbitrary constants, is –

• A. $\frac{d^{2}y}{dx^{2}}$ + 8 $\frac{dy}{dx}$ + 15 y = 0
• B. $\frac{d^{2}y}{dx^{2}}$ – 8 $\frac{dy}{dx}$ + 15 y = 0
• C. $\frac{d^{2}y}{dx^{2}}$ – $\frac{dy}{dx}$ + y = 0
• D. None of these

Answer 1

Answer: (B)

$\frac{d^{2}y}{dx^{2}}$ – 8 $\frac{dy}{dx}$ + 15 y = 0

Answer 2

y = Ae^3x + Be^5x .... (1)

$\frac{dy}{dx}$ = 3Ae^3x + 5Be^5x ....(2)

$\frac{d^{2}y}{dx^{2}}$ = 9Ae^3x + 25Be^5x ....(3)

Eliminates A & B from (1), (2) and (3) $\frac{d^{2}y}{dx^{2}}$ = $\frac{8dy}{dx}$ – 15 y