Project ForgeEngineering Mathematics
Differential Equations
GATE 2009
Medium
The inverse Laplace transform of 1/(2s²+3s+1) is
- e^(−t/2)−e⁻ᵗ
- B2e^(−t/2)−e⁻ᵗ
- Ce⁻ᵗ−2e^(−t/2)
- De⁻ᵗ−e^(−t/2)
Explanation
2s²+3s+1=(2s+1)(s+1). Partial fractions: 1/[(2s+1)(s+1)]=2/(2s+1)−1/(s+1)=1/(s+0.5)−1/(s+1). Inverse: e^(−t/2)−e⁻ᵗ.
Source: GATE CH 2009 (2009)
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