Question

Consider the ODE :



y"'-3y''+2y'=10 + 4xe^(2x).

Solve, this Differential equation.

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Answer 1

Final Result :
General Solution :

$y = c(1) + c(2) {e}^{x} + c(3) {e}^{2x} + \\ 5x + {e}^{2x} ( {x}^{2} - 3x)$


Concepts to know :

1) Method of undetermined Co efficient to solve 2nd order
Non-homogeneous equation.


2) Annihilator method (Method -2 to get particular solution)


3)Solution of homogeneous equations.



Steps are given in pic :

For Calculation : See Pic attached to it.


Hope, you understand my answer and it may helps you.

Answer 2

Answer:

Plz refer to the attachment for the answer.