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Chapter 4: Q8E (page 180)

Decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation. ty''-y'+2y=sin3t

Short Answer

Expert verified

No, the method of undetermined coefficients can鈥檛 be applied.

Step by step solution

01

Use the method of undetermined coefficients to find a particular solution of a given differential equation.

Given equation isty''-y'+2y=sin3t.

Here, the given differential equation is non-homogeneous.

According to the method of undetermined coefficients, the method of undetermined coefficients applies to the differential equation of the following form,

ay''+by'+cy=f(t)

Here, a, b and c are the constants.

02

Final conclusion.

The coefficient ofy'' is twhich is not constant. Therefore, we can say that L.H.S. of the given equation is not a differential equation with a constant coefficient.

Thus, the method of undetermined coefficients cannot be applied.

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