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Chapter 4: Q7E (page 180)

Decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation.8z'(x)-2z(x)=3x100e4xcos25x

Short Answer

Expert verified

Yes, the method of undetermined coefficients can be applied.

Step by step solution

01

Use the method of undetermined coefficients.

Given equation,

8z'(x)-2z(x)=3x100e4xcos25x鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�.....(1)

According to the method of undetermined coefficients,

To find a particular solution to the differential equation;

ay''+by'+cy=Ctme伪迟肠辞蝉尾迟鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�orCtme伪迟蝉颈苍尾迟

For,尾鈮�0 use the form:

yp(x)=ts(Amtm+...+A1t+A0)e伪迟肠辞蝉尾迟+ts(Bmtm+...+B1t+B0)e伪迟蝉颈苍尾迟

02

Final conclusion.

Compare with the given differential equation,

8z'(x)-2z(x)=3x100e4xcos25x

We have,

尾=25鈮�0

Therefore, the method of undetermined coefficients can be applied.

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