The general solution of the differential equation d 2 y d x 2 -8 dy dx -16y-0 is

The correct option is C ( A+Bx ) e ^ 4x Given equation is d ^ 2 y d x ^ 2 +8 dy dx +16y=0 Auxillary equation is m ^ 2 +8m+16=0 ⇒ (m+4) ...

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Standard XII

Mathematics

Higher Order Derivatives

The general s...

Question

The general solution of the differential equation $\frac{d^{2} y}{d x^{2}} + 8 \frac{d y}{d x} + 16 y = 0$ is

(A + B x) e^{5 x}

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(A + B x) e^{- 4 x}

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(A + B x^{2}) e^{4 x}

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(A + B x^{4}) e^{4 x}

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Solution

The correct option is C $(A + B x) e^{- 4 x}$
Given equation is
$\frac{d^{2} y}{d x^{2}} + 8 \frac{d y}{d x} + 16 y = 0$
Auxillary equation is $m^{2} + 8 m + 16 = 0$
$\Rightarrow {(m + 4)}^{2} = 0 \Rightarrow m = - 4$
$∴$ Solution is $(A + B x) e^{- 4 x}$

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The general solution of the differential equation d2ydx2+8dydx+16y=0 is

The correct option is C (A+Bx)e−4xGiven equation isd2ydx2+8dydx+16y=0Auxillary equation is m2+8m+16=0⇒(m+4)2=0⇒m=−4∴ Solution is (A+Bx)e−4x

The general solution of the differential equation $\frac{d^{2} y}{d x^{2}} + 8 \frac{d y}{d x} + 16 y = 0$ is

The correct option is C $(A + B x) e^{- 4 x}$
Given equation is
$\frac{d^{2} y}{d x^{2}} + 8 \frac{d y}{d x} + 16 y = 0$
Auxillary equation is $m^{2} + 8 m + 16 = 0$
$\Rightarrow {(m + 4)}^{2} = 0 \Rightarrow m = - 4$
$∴$ Solution is $(A + B x) e^{- 4 x}$