Question:
A particular integral of the differential equation
\[
y'' + 3y' + 2y = e^{ex}
\]
is
A particular integral of the differential equation
\[ y'' + 3y' + 2y = e^{ex} \] is
\[ y'' + 3y' + 2y = e^{ex} \] is
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In solving non-homogeneous differential equations, use undetermined coefficients or variation of parameters to find the particular solution.
Updated On: Dec 11, 2025
- \( e^{ex} e^{-x} \)
- \( e^{ex} e^{-2x} \)
- \( e^{ex} e^{2x} \)
- \( e^{ex} e^x \)
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The Correct Option is B
Solution and Explanation
Step 1: Solving the non-homogeneous differential equation.
The given equation is a second-order linear differential equation with constant coefficients. We solve the corresponding homogeneous equation and then find the particular integral using the method of undetermined coefficients.
Step 2: Finding the particular integral.
The correct form of the particular integral is \( e^{ex} e^{-2x} \), as determined by the method of undetermined coefficients.
Step 3: Conclusion.
The correct answer is (B) \( e^{ex} e^{-2x} \).
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