Mathematics · Calculus of Variations
Find the curve that extremizes the functional I(y) = ∫01 [(dydx)2 + 12xy] dx for the given boundary conditions y(0) = 0 and y(1) = 1.
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1y = 3x3 - 2x2
- 2y = 2x2 - x
- 3y = x2
- 4y = x3✓
Correct answer
y = x3
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