Question:
If y=e⁻ˣ x and y+k y'=0, where y₄=d⁴ydx⁴, then k=
If y=e⁻ˣ x and y+k y'=0, where y₄=d⁴ydx⁴, then k=
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Use characteristic equation for exponential–trigonometric functions.
Updated On: Mar 17, 2026
- 4
- -4
- 2
- -2
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The Correct Option is D
Solution and Explanation
Given y=e⁻ˣ x.
Characteristic equation:
(D+1)²+1=0 D²+2D+2=0
Thus the differential equation is:
y''+2y'+2y=0
Differentiating twice more:
y⁽⁴⁾+2y⁽³⁾+2y''=0
y⁽⁴⁾=-2y⁽³⁾-2y''
Comparing with y₄+ky=0, we get:
k=-2
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