Question

If $y=e^{4x}+2e^{-x}$ satisfied the equation $\frac{d^{3}y}{d{x}^3}+A\frac{dy}{dx}+By=0$ then value of $|A+B|$ is

• A. $36$
• B. $25$
• C. $24$
• D. $15$

Answer 1

The correct option is B $25$

$\frac{d^{3}y}{d{x}^3}$ = $64e^{4x}$ - $2e^{-x}$

$\frac{dy}{dx}$ = $4e^{4x}$ - $2e^{-x}$

$\frac{d^{3}y}{d{x}^3}$ + $A$$\frac{dy}{dx}$ + $By$ = 0

$\Rightarrow$ $e^{4x}(64+4A+B)$ + $2e^{-x}(-1-A+B)$ = 0

64 +4A + B = 0 -(I)

-1 - A + B = 0 -(II)

Solving (i) and (ii),

A = -13 ; B = -12

$\therefore$ $|A+B|$ = $25$

So, the correct option is 'B'.