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Exploring a Particular Solution. Your sketch currently displays a point P and a line passing through it. The line represents the local slope at P determined by a given differential equation. While the differential equation has many (in fact, an infinite number) of solutions, only one of these solutions passes through P.

The general solution of the differential equation is expressed as follows The described algorithm is called the method of variation of a constant. Of course, both methods lead to the same solution.

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Diﬀerential equations are called partial diﬀerential equations (pde) or or-dinary diﬀerential equations (ode) according to whether or not they contain partial derivatives. The order of a diﬀerential equation is the highest order derivative occurring. A solution (or particular solution) of a diﬀerential equa-

the solution for the differential equation. The next few examples barely begin to explore differential equations on the 50g. Practice solving differential equations Example 1: The differential equation of the concentration c(t) of a chemical substance that undergoes decay in a first order reaction is given by:

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New in Mathematica 10 › Enhanced Calculus & Differential Equations › Find Symbolic Solutions for Delay Differential Equations Solve a first-order delay equation using DSolve .

March 2, 2009 MathExcel Worksheet # 16: Separable Diﬀerential Equations 1. Solve the following diﬀerential equations. (a) y0 = x ey (b) (x2 +1)y0 = xy (c) dy dx +ex+y = 0 2. Solve the following initial value problems.