Verify that the function y=e^{-3x} is a solution to the

Roger Smith 2021-12-18 Answered
Verify that the function y=e3x is a solution to the differential equation d2ydx2+dydx6y=0?
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Becky Harrison
Answered 2021-12-19 Author has 40 answers
Step 1
To verify the function y=e3x is a solution of the differential equations d2ydx2+dydx6y=0.
That is the function y=e3x satisfies the equation d2ydx2+dydx6y=0 ...(1)
Step 2
Now, dydx=ddx(e3x)=e3x(3)=3e3x
d2ydx2=ddx3(e3x)=(3)ddx(e3x)=3(e3x(3))=9e3x
6y=6e3x
Therefore, d2ydx2+dydx6y
=9e3x3e3x6e3x
=9e3x9e3x
=0
Hence, equation (1) satisfies.
Therefore, the given function y=e3x is a solution to the given differential equation.
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Orlando Paz
Answered 2021-12-20 Author has 42 answers
Given, y=e3x
On differentiating with x, we get
dydx=3e3x
On differentiating again with x, we get
d2ydx2=9e3x
Now let's see what is the value of d2ydx2+dydx6y
=9e3x3e3x6e3x
=0
Conclusion: Therefore, y=e3x is the solution of d2ydx2+dydx6y=0
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RizerMix
Answered 2021-12-29 Author has 438 answers

y=e3x
Differentiating with x
dydx=3e3x
Again differentiating, d2ydx2=9e3x
Substituting in d2ydx2+dydx6y
9e3x3e3x(6e3x)=0
Hence y=e3x is a solution.

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