By Dennis G. Zill
The scholar strategies guide to Accompany complex Engineering arithmetic, 6th variation is designed that will help you get the main from your path Engineering arithmetic direction. It offers the solutions to each 3rd workout from every one bankruptcy on your textbook. this allows you to evaluate your development and realizing whereas encouraging you in finding options by yourself. scholars, use this software to: - money solutions to chose workouts - be sure that you simply comprehend rules and ideas - evaluate prior fabric - organize for destiny fabric Get the main from your complicated Engineering arithmetic path and enhance your grades together with your scholar recommendations guide!
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Extra info for Student Solutions Manual to Accompany Advanced Engineering Mathematics
From fx = x3 + y 3 we obtain f = 14 x4 + xy 3 + h(y), h (y) = 0, and h(y) = 0. A solution is 14 x4 + xy 3 = c. 11. Let M = y ln y − e−xy and N = 1/y + x ln y so that My = 1 + ln y + xe−xy and Nx = ln y. The equation is not exact. 12. Let M = 3x2 y + ey and N = x3 + xey − 2y so that My = 3x2 + ey = Nx . From fx = 3x2 y + ey we obtain f = x3 y + xey + h(y), h (y) = −2y, and h(y) = −y 2 . A solution is x3 y + xey − y 2 = c. 13. Let M = y − 6x2 − 2xex and N = x so that My = 1 = Nx . From fx = y − 6x2 − 2xex we obtain f = xy − 2x3 − 2xex + 2ex + h(y), h (y) = 0, and h(y) = 0.
From the phase portrait we see that the solution curve is decreasing when y < 3 and increasing when y > 3. 3 y 8 2 2 2 4 3 2 -4 -2 2 x 4 -2 (b) Separating variables and integrating we obtain y 8 (y − 3) dy = dx 1 2 y − 3y = x + c 2 y 2 − 6y + 9 = 2x + c1 6 4 2 (y − 3)2 = 2x + c1 √ y = 3 ± 2x + c1 . 2 Separable Variables The initial condition dictates whether to use the plus or minus sign. √ When y1 (0) = 4 we have c1 = 1 and y1 (x) = 3 + 2x + 1 . √ When y2 (0) = 2 we have c1 = 1 and y2 (x) = 3 − 2x + 1 .
When y1 (0) = 4 we have c1 = 1 and y1 (x) = 3 + 2x + 1 . √ When y2 (0) = 2 we have c1 = 1 and y2 (x) = 3 − 2x + 1 . √ When y3 (1) = 2 we have c1 = −1 and y3 (x) = 3 − 2x − 1 . √ When y4 (−1) = 4 we have c1 = 3 and y4 (x) = 3 + 2x + 3 . 39. (a) Separating variables we have 2y dy = (2x + 1)dx. Integrating gives y 2 = x2 + x + c. When y(−2) = −1 we √ ﬁnd c = −1, so y 2 = x2 + x − 1 and y = − x2 + x − 1 . The negative square root is chosen because of the initial condition. 65). 1 -5 -4 -3 -2 -1 -1 1 2 x -2 -3 -4 -5 √ (c) Solving x + x − 1 = 0 we get x = ± 5 , so the largest interval of deﬁnition is (−∞, − 12 − 12 5 ).
Student Solutions Manual to Accompany Advanced Engineering Mathematics by Dennis G. Zill