chapter2.page08

chapter2.page08 - of change of the temperature T ( t ) of a...

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8 1. EXPLICITLY SOLVABLE FIRST ORDER DIFFERENTIAL EQUATIONS Project 3. Linear equations and Bernoulli equations 3.1. Linear Equations. An ODE of form y 0 + a ( x ) y = b ( x ) is called a linear equation. Any equation that can be converted into this form can also be called a linear equation. Such as x 2 y 0 + 4 x 2 e x y = sin( x ), which can be written as y 0 + e x y = sin( x ) x 2 , is a linear equation. The general solution of the linear equation is y ( x ) = e R a ( x ) dx ˆ Z b ( x ) e - R a ( x ) dx dx + C ! Notice that C is inside the parenthesis. It is common mistake of students forgetting multiplying C by e R a ( x ) dx . Example 3.1 . According to Newton’s law of cooling, the time rate
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Unformatted text preview: of change of the temperature T ( t ) of a air conditioned house with ex-ternal temperature A ( t ) is proportional to the dierence A-T . That is, dT t = k ( A-T ) , where k is positive constant. Now, suppose A ( t ) = 80-10cos( t ) nd the general solution. Solution Since we want to use Mathcad to nd the antiderivative for us, the rst thing is to nd how to get the Greek letter . To get , rst bring the math tool bar from the View menu Figure 3. Math Toolbar...
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