Particular solution

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  This solution is comprised of a detailed explanation to answer how do I find the corresponding particular solution that satisfies the initial condition y = 1 when x = 0 and what is the value of y given by this particular solution when x = 7.

• Particular solution of differential equation : d²y/dx² - y = xe^x

  72396 Particular solution of differential equation The differential equation is: d²y/dx² - y = xe^x For the first part of the general solution, I got y=Ae^x + Be^-x where a and b are constants. Now I need to find the particular solution.

• Second order differential equation

  Let and , then a particular solution of the ODE is Therefore, a particular solution is This shows how to find a particular solution for a given differential equation.

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  We set the particular solution to be the homogenous solution of , namely: (3.7) We plug it back into equation (1.1): The particular solution is: simply: (3.8)   The general solution of equation (3.1) is the sum of a linear combination

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  Now we need to find a particular solution to d²y/dx² - 4y = e^(3x). We can assume that the particular solution has a form where c is a constant to be determined.

• Particular solution of the differential equation

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  Now identify the particular solution of (1). 2). Using the Method of Undetermined coefficients find a particular solution of y''+y = x2 + sin(x) 3).

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  A particular solution of a differential equation is found. The particular solution of the differential equation satisfying the given conditions is examined.