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Chapter 4: Q15E (page 186)

Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation.

y''+ety'+y=7+3t

Short Answer

Expert verified

No,the method of undetermined coefficients cannot be applied.

Step by step solution

01

Use the method of undetermined coefficients. 

Given equation,

y''+ety'+y=7+3t

Here, the given differential equation is non-homogeneous.

According to the method of undetermined coefficients, the method of undetermined coefficients applies only to non-homogeneities that are polynomials, exponentials, sine, cosine, or products of these functions.

And the left-hand side consists of the differential equation with constants coefficients.

02

Conclusion

The L.H.S. of the equationhas a non-constantcoefficient (et).

So, the method of undetermined coefficients cannot be applied.

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