Lab1_Solutions

Lab1_Solutions - MATH 138 Maple Lab Assignment 1...

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Unformatted text preview: MATH 138 Maple Lab Assignment 1 Differential Equations in Maple O with DEtools : O ode1 d diff y x , x = x C y x ; ode1 := O dsolve O dsolve O dsolve ode1, y 0 = 1 ode1, y 0 =K 1 ode1, y 0 =K 2 ; y x = K K x C 2 ex 1 ; y x = K Kx 1 ; y x = K K x K ex 1 O DEplot ode1, y x , x =K ..3, y =K ..3, y 0 = 1 , y 0 =K , y 0 =K , linecolour 3 3 1 2 = black ; d y x = x Cy x dx 3 2 y(x) 1 K 3 K 2 K 1 0 1 x 2 3 K 1 K 2 K 3 1 O ode2 d diff y x , x = y x K 1 $ 4 K y x ; d ode2 := y x = y x K1 dx O dsolve ode2, y 0 = 5 ; K 4 Ky x yx = KCe 16 K 2 3 x 2 e O dsolve ode2, y 0 = 2 ; yx = O dsolve ode2, y 0 = 0.5 ; yx = O DEplot ode2, y x , x =K ..3, y = 0 ..6, 3 = black ; 2 3 x 2 K4 2 2 e3 x K I π K 1 e3 x K I π K 2 4 e3 x K 7 e3 x K 7 y 0 = 5 , y 0 = 2 , y 0 = 0.5 , linecolour 6 5 4 y(x) 3 2 1 K 3 K 2 K 1 0 1 x 2 3 QUESTION: Your solution y that starts with y 0 = 2 seems to have its steepest slope when y = 2.5. Explain briefly how this can be predicted directly from the given differential equation. ANSWER: The function y K 1 dy = y K1 dx 4 K y is a parabola with a maximum at y = 4 C1 2 = 2.5. Thus the slope 4 K y has to be a maximum when y = 2.5. 2 ...
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Lab1_Solutions - MATH 138 Maple Lab Assignment 1...

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