3. (UD-2) Use the method of undetermined coefficients to find the general solution to the following equation: y" - 10y' + 25y = 50x² + 6e5

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3. **(UD-2)** Use the method of undetermined coefficients to find the general solution to the following equation:

\[ y'' - 10y' + 25y = 50x^2 + 6e^{5x} \]

This problem involves solving a second-order linear differential equation with constant coefficients using the method of undetermined coefficients. The equation has a non-homogeneous part consisting of a polynomial term \(50x^2\) and an exponential term \(6e^{5x}\). The solution will be a combination of the homogeneous solution and a particular solution accounting for the non-homogeneous part.
Transcribed Image Text:3. **(UD-2)** Use the method of undetermined coefficients to find the general solution to the following equation: \[ y'' - 10y' + 25y = 50x^2 + 6e^{5x} \] This problem involves solving a second-order linear differential equation with constant coefficients using the method of undetermined coefficients. The equation has a non-homogeneous part consisting of a polynomial term \(50x^2\) and an exponential term \(6e^{5x}\). The solution will be a combination of the homogeneous solution and a particular solution accounting for the non-homogeneous part.
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