Project ForgeEngineering Mathematics
Calculus
GATE 2017
Medium
Consider the differential equation 3y″(x)+27y(x)=0 with initial conditions y(0)=0 and y′(0)=2000. The value of y at x=1 is __________.
94.1(± 1 accepted)
Explanation
y″+9y=0 has general solution y = A sin(3x) + B cos(3x), with ω=3. y(0)=0 gives B=0. y′(x)=3A cos(3x), so y′(0)=3A=2000 → A=666.67. y(1)=666.67·sin(3)≈666.67×0.14112≈94.1.
Source: GATE ME 2017 Session 2 (ME-2) (2017)
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