Unformatted text preview: G ( x, y ) = xe y − ye y + e y = c or x = y − 1 + ce − y . EXERCISES 2.6: Substitutions and Transformations, page 78 1. We can write the equation in the form dy dx = ( y − 4 x − 1) 2 = [( y − 4 x ) − 1] 2 = G ( y − 4 x ) , where G ( t ) = ( t − 1) 2 . Thus, it is of the form dy/dx = G ( ax + by ). 3. In this equation, the variables are x and t . Its coeﬃcients, t + x + 2 and 3 t − x − 6, are linear functions of x and t . Therefore, given equation is an equation with linear coeﬃcients. 79...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Derivative, Trigraph, ey dy, c. ey dx

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