GATE 2018 CE (CE1) – Question 49
Gradually varied depth satisfies $$\frac{dy}{dx}=\frac{1-e^{-(10/3)\ln y}}{250-45e^{-3\ln y}}.$$ Starting at y(0) = 0.8 m, use one single-step Euler calculation to x = 1 m. Depth, to three decimals, is ______ m.
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Correct answer: 0.78 to 0.80
Explanation
Rewrite the slope as $F(y)=(1-y^{-10/3})/(250-45y^{-3})$. At y = 0.8, $F=-0.00680985$. One Euler step of length 1 gives $y_1=0.8+1(-0.00680985)=0.793190$ m, or 0.793 m.