What is the free response of the differential equation d^2y/dt^2-7dy/dt +10y = u, with initial condition y(0)=0 and dy/dt(t=0) = 6 ? d²y -7 dy +10y = u dt² dt initial conditions y(0) = 0, (dy/dt),-o = 6 Ya(t) = e5t - e2t option 1 Ya(t) = -2e5t2e²t Option 3 Ya(t) = 2e5t2e²t O Option 2 ya(t)=e5t + e²t Option 4

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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What is the free response of the differential equation d^2y/dt^2-7dy/dt +10y
= u, with initial condition y(0)=0 and dy/dt(t=0) = 6 ?
d²y
dt²
-7 dy + 10y = u
dt
initial conditions y(0) = 0, (dy/dt),-o = 6
Ya(t) = e5t - e2t
O option 1
Ya(t) = -2e5t2e²t
Option 3
Ya(t) = 2e5t - 2e²t
Option 2
Ya(t) = e5t + e²t
Option 4
Transcribed Image Text:What is the free response of the differential equation d^2y/dt^2-7dy/dt +10y = u, with initial condition y(0)=0 and dy/dt(t=0) = 6 ? d²y dt² -7 dy + 10y = u dt initial conditions y(0) = 0, (dy/dt),-o = 6 Ya(t) = e5t - e2t O option 1 Ya(t) = -2e5t2e²t Option 3 Ya(t) = 2e5t - 2e²t Option 2 Ya(t) = e5t + e²t Option 4
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