# If a particular integral of the differential equation #(D^2+2D-1)y=e^(ax)# is #(-4/7)e^(ax)# then the value of a is ?

# a=-3/2, -1/2# #We cannot eliminate a solution, thus we are left with two possibilities

# y = Ae^((-1-sqrt(2))x) + Be^((-1+sqrt(2))x) -4/7e^(-3/2x) # or

# y = Ae^((-1-sqrt(2))x) + Be^((-1+sqrt(2))x) -4/7e^(-1/2x) #

We have:

Alternatively, in standard form:

Complementary Role

The equation homogeneous linked to [A] is

Additionally, the related auxiliary equation is:

Consequently, the homogeneous equation's solution is:

Specific Resolution

We would search for a solution of the following form in order to identify a specific solution of the non-homogeneous equation:

When we replace the DE [A] with:

or

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To find the value of ( a ) in the given differential equation ( (D^2+2D-1)y=e^{ax} ) when the particular integral is ( (-\frac{4}{7})e^{ax} ), we can use the method of undetermined coefficients. By substituting ( y_p = Ae^{ax} ) into the differential equation, we can determine the value of ( a ). Comparing coefficients, we find that ( a = 1 ).

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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.

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