What is the particular solution of the differential equation? : #y'+4xy=e^(-2x^2)# with #y(0)=-4.3#
# y = (x-4.3)e^(-2x^2) #
We have:
We can use an integrating factor when we have a First Order Linear non-homogeneous Ordinary Differential Equation of the form;
The given equation is already in standard form, so the integrating factor is given by;
Which we can now "seperate the variables" to get:
Which is trivial to integrate giving the General Solution:
Applying the initial condition we get:
Giving the Particular Solution:
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The particular solution of the given differential equation is:
[ y(x) = e^{-2x^2} - 4.3 - \frac{1}{2}x^2 e^{-2x^2} ]
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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