Project ForgeEngineering Mathematics
Differential Equations
GATE 2020
Medium
Given dy/dx=y−20, and y|x=0=40, the value of y at x=2 is (round off to nearest integer)
168(± 4 accepted)
Explanation
d/dx(y·e^(−x))=−20e^(−x) ⟹ y·e^(−x)=20e^(−x)+C ⟹ y=20+Ce^x. At x=0: 40=20+C ⟹ C=20. y(x)=20+20e^x. At x=2: y=20+20e²=20+147.78=167.78≈168.
Source: GATE CH 2020 (2020)
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