Mathematics · Partial Differential Equations
If u(x, t) is the solution of the initial value problem:
ut = uxx, x ∈ &DoubleStruckCapitalR;, t > 0
u(x, 0) = sin(4x) + x + 1, x ∈ &DoubleStruckCapitalR;
satisfying |u(x, t)| < 3ex2 for all x ∈ &DoubleStruckCapitalR; and t > 0, then:
ut = uxx, x ∈ &DoubleStruckCapitalR;, t > 0
u(x, 0) = sin(4x) + x + 1, x ∈ &DoubleStruckCapitalR;
satisfying |u(x, t)| < 3ex2 for all x ∈ &DoubleStruckCapitalR; and t > 0, then:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1u(π/8, 1) = -u(-π/8, 1)
- 2u(π/8, 1) + 2u(-π/8, 1) = 2
- 3u(π/8, 1) = u(-π/8, 1)
- 4u(π/8, 1) + u(-π/8, 1) = 2✓
Correct answer
u(π/8, 1) + u(-π/8, 1) = 2
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