Project ForgeEngineering Mathematics
Differential Equations
GATE 2010
Medium
The solution of the differential equation d²y/dt²+2dy/dt+2y=0 with initial conditions y(0)=0, dy/dt|t=0=−1, is
- A−t sin t
- B−e⁻ᵗ(1−cos t)
- C−(t+sin t)/2
- −e⁻ᵗ sin t
Explanation
Characteristic equation r²+2r+2=0 gives r=−1±i. General solution y=e⁻ᵗ(A cos t+B sin t). y(0)=0⟹A=0. y=Be⁻ᵗsin t; y'=Be⁻ᵗ(cos t−sin t); y'(0)=B=−1. So y=−e⁻ᵗsin t.
Source: GATE CH 2010 (2010)
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