Unformatted text preview: C = 3. Hence x ( t ) = t 2 + 3 . Notice if we drop the C from (1), we would not be able to ﬁnd x ( t ) that satisﬁes x (0) = 3! a The problem of ﬁnding a particular solution with initial condition is called initial value problem, which we will discuss in the later section. a Practice 1. Find the following deﬁnite integral using Mathcad . (a) R 2-1 x 3-x cos( x 2 + 1) dx (b) R 4 1 x 3 +4 x-5 x +1 dx (c) R-5 e 3 x-x x 2 +3 dx (d) R 10-1 x 2-x sec( x 2 + 1) dx 2. Find the following indeﬁnite integral using Mathcad . (a) R x 5-x p ( x 2 + 1) dx (b) R x 3 +4 x-5 x 2 +1 dx...
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- Spring '11
- Derivative, dx, ORDER DIFFERENTIAL EQUATIONS, exp3x + cos, auto execution mode