MathAnalysisDifferential equations

Higher-order linear differential equations

Guess the form of a particular solution

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The right side of some nonhomogeneous ODE is $f(x) = e^x(x^3 + x)$ .

What is the general form of its particular solution?

Select one option from the list

Ae^x(Bx^3 + Cx^2 + Dx + E)

e^x(Ax^3 + Bx^2 + Cx)

Ae^x

e^x(Ax^3 + Bx)

Ax^3 + Bx^2 + Cx + D

e^x(Ax^3 + Bx^2 + Cx + D)

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