Mathematics · Partial Differential Equations
मान लीजिए कि u(x, t) निम्नलिखित प्रारंभिक-सीमा मान समस्या (initial-boundary value problem) का समाधान है: ∂u∂t = ∂2u∂x2, x ∈ (0, π), t > 0, u(0, t) = u(π, t) = 0, u(x, 0) = sin(4x) cos(3x). तो, प्रत्येक t > 0 के लिए, u(π4, t) का मान क्या होगा?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1e-49t4√2 (1 - e48t)
- 2e-49t2√2 (1 + e48t)
- 3e-49t2√2 (1 - e48t)✓
- 4e-49t2√2 (e48t - 1)
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e-49t2√2 (1 - e48t)
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