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  4. The elimination of constants A, B and C from y = A + Bx - Ce-x leads the differential equation:

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

Differential Equations

Solution:

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