Can find the p.I of higher order equation d^3+2d^2+d= e^x+x+x^2+sinx

To find the particular integral (P.I.) of the higher-order differential equation

\[
d^3 + 2d^2 + d = e^x + x + x^2 + \sin x,
\]

where \( d \) represents the differential operator \( \frac{d}{dx} \), we proceed by solving the equation using the method of undetermined coefficients.

### Step 1: Operator applied to the right-hand side components

The general form of

Learn how to find the particular integral (P.I.) of the differential equation d^3 + 2d^2 + d = e^x + x + x^2 + sin x using the method of undetermined coefficients. This problem involves solving a higher-order differential equation and understanding the application of differential operators. Suitable for college-level students and those studying differential equations.

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