Question
Download Solution PDFThe function y = e-4x is a solution to the differential equation
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Some useful formulas are:
\(\rm{ d(e^{ax})\over dx } = ae^{ax}\)
Calculation:
Given function is
y = e-4x, differentiating it we get
\(\rm{ dy\over dx } = -4e^{-4x}\)
Differentiating it further we get,
\(\rm{ d^2y\over dx^2 } = 16e^{-4x}\)
Now, \(\rm{ d^2y\over dx^2 }+3 { dy\over dx }-4y=0\)
=\(\rm 16e^{-4x}+3(-4e^{-4x})-4e^{-4x}\)
= 0
So, \(\rm{ d^2y\over dx^2 }+3 { dy\over dx }-4y=0\)
Last updated on May 19, 2025
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