For example if we want to find a particular solution

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For example, if we want to find a particular solution ψ for the equation ay 00 + by 0 + cy = sin( x ) + e 5 x Then we need only find a particular solution ψ 1 to the equation ay 00 + by 0 + cy = sin( x ) (which we can do by Case 3), and a particular solution ψ 2 to the equation ay 00 + by 0 + cy = e 5 x (which we can do by Case 2), and the solution we want is just their sum: ψ = ψ 1 + ψ 2 .
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