Let a,b be constants. The differential equation: x' (t) = ax(t) + b Has the solution: x(t) = xt * e-a(T-t) Where XT = x(T) is a constant. - ST ₂-a(v-t) bdv e a) Verify that the solution expression solves the differential equation.
Let a,b be constants. The differential equation: x' (t) = ax(t) + b Has the solution: x(t) = xt * e-a(T-t) Where XT = x(T) is a constant. - ST ₂-a(v-t) bdv e a) Verify that the solution expression solves the differential equation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let a,b be constants.
The differential equation:
x' (t) = ax(t) + b
Has the solution:
x(t) = xt * e-a(T-t)
Where
XT = x(T)
is a constant.
- ST ₂-a(v-t) bdv
e
a) Verify that the solution expression solves the differential equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c5c41cf-1a95-4095-a510-8904b76f835a%2Fbb704e36-4d51-4289-a1e6-da5da4ef9eb0%2Fetgmg5h_processed.png&w=3840&q=75)
Transcribed Image Text:Let a,b be constants.
The differential equation:
x' (t) = ax(t) + b
Has the solution:
x(t) = xt * e-a(T-t)
Where
XT = x(T)
is a constant.
- ST ₂-a(v-t) bdv
e
a) Verify that the solution expression solves the differential equation.
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