(B) Sketch a solution curve that passes through the point (0, 1) on your slope field. (C) Find the particular solution to the differential equation with the initial condition y f f = (x) (0) =1. (D) Sketch a solution curve that passes through the point on your slope field. (0, −1) (E) Find the particular solution to the differential equation with the initial condition y f f = (x) (0) = −1. Solutions: 1. y(1)=3.187 2. y(2) = 3.014 3. y(1) = 0.501 4. y(5) = 19.42. Thus, there is approximately 19 fish after 5 weeks. 5. the error is clearly getting much worse as increases. t Time, Approximation Exact Error tn = 0 =1 = 1 0 % t0 y0 y(0)
(B) Sketch a solution curve that passes through the point (0, 1) on your slope field. (C) Find the particular solution y = f (x) to the differential equation with the initial condition f (0) =1. (D) Sketch a solution curve that passes through the point (0, −1) on your slope field. (E) Find the particular solution y = f (x) to the differential equation with the initial condition f (0) = −1. Solutions: 1. y(1)=3.187 2. y(2) = 3.014 3. y(1) = 0.501 4. y(5) = 19.42. Thus, there is approximately 19 fish after 5 weeks. 5. the error is clearly getting much worse as t increases. Time, tn Approximation Exact Error t0 = 0 y0 =1 y(0) = 1 0 %
EULER%20and%20SLOPE%20FIELDS-HANDOUT.docx