Certain indefinite integrals such as dx cannot be expressed in finite terms using elementary functions. When such an integral is encountered while solving a differential equation, it is often helpful to use definite integration (integrals with variable upper limit). Use separation of variables and definite integration to find an explicit solution to the initial value problems in parts a - c, and use Simpson's rule with n = 4 to approximate an answer to part b at x = 0.5 to three decimal places. Click the icon to view an example of this process. dy x2 = e dx a. Solve the initial value problem with y(0) = 4. Use t as the variable of integration in the explicit solution. y(x) =

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.