Question

The elimination of constants A, B and C from $y=A+Bx-C{e}^{-x}$ leads the differential equation:

• A. y" + y"' = 0
• B. y" - y"' = 0
• C. y' + ex = 0
• D. y" + ex = 0

Answer 1

Answer: (A)

Given, $y=A+Bx-C{e}^{-x}$
$\Rightarrow y^{\prime }=B+C.e^{-x}$ ..... (i)
and $y"=-C{e}^{-x}$.... (ii)
and $y{"}^{\prime }=C{e}^{-x}$ ... (iii)
From equ. (ii) and (iii),
y"' = - y" $\Rightarrow$ y"' + y" = 0