This is a question about Ordinary Differential Equations. For solving linear differential equations, I have seen people use...

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This is a question about Ordinary DifferentialEquations.
For solving linear differential equations, I have seenpeople use the method of integrating factors and the method ofvariation of parameters.
Is it true that either of these 2 methods can be usedto solve any linear differential equation?
If so, could you show me an example where a lineardifferential equation is solved using both of these methods.
If not, could you explain using examples as to whythis is the case? For example, does it depend on thecomplicatedness of the equation etc.
Thank you.

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For solving a linear differential equation whether to usemethod of integrating factors and the method of variation ofparameters we should consider some of the conditions like To apply method of integrating factors the linear differentialequation should be of a first order linear differential See Answer

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