9-2 Eulers Method.sagews

var('P t')
plot_slope_field(0.08*P*(1 - 0.001*P), (t, 0, 500), (P, -500, 2000), plot_points = 25)

(P, t)

var('x y')
plote2-us/26769/tmp_ucbBch.svg","show":true,"text":null,"uuid":"a7427573-a5a7-4b4a-b129-f1f6beff5719"},"once":false}

var('x y')
eulers_method(x - y, 0, 1, 0.1, 2.5)

(x, y) x y h*f(x,y) 0 1 -0.100000000000000 0.100000000000000 0.900000000000000 -0.0800000000000000 0.200000000000000 0.820000000000000 -0.0620000000000000 0.300000000000000 0.758000000000000 -0.0458000000000000 0.400000000000000 0.712200000000000 -0.0312200000000000 0.500000000000000 0.680980000000000 -0.0180980000000000 0.600000000000000 0.662882000000000 -0.00628820000000000 0.700000000000000 0.656593800000000 0.00434062000000000 0.800000000000000 0.660934420000000 0.0139065580000000 0.900000000000000 0.674840978000000 0.0225159022000000 1.00000000000000 0.697356880200000 0.0302643119800000 1.10000000000000 0.727621192180000 0.0372378807820000 1.20000000000000 0.764859072962000 0.0435140927038000 1.30000000000000 0.808373165665800 0.0491626834334200 1.40000000000000 0.857535849099220 0.0542464150900780 1.50000000000000 0.911782264189298 0.0588217735810702 1.60000000000000 0.970604037770368 0.0629395962229632 1.70000000000000 1.03354363399333 0.0666456366006669 1.80000000000000 1.10018927059400 0.0699810729406002 1.90000000000000 1.17017034353460 0.0729829656465402 2.00000000000000 1.24315330918114 0.0756846690818862 2.10000000000000 1.31883797826303 0.0781162021736976 2.20000000000000 1.39695418043672 0.0803045819563278 2.30000000000000 1.47725876239305 0.0822741237606950 2.40000000000000 1.55953288615375 0.0840467113846255 2.50000000000000 1.64357959753837 0.0856420402461630

# ics = initial condition, end_points = interval
var('x y')
desolve_rk4(x + y, y, ics=[0, 0], end_points=[-3, 3], output='slope_field')

(x, y)

desolve_rk4(x*(y^2-4), y, ics=[0, 1], end_points=[-5, 5], output='slope_field')

var('y')
plot_slope_field(.08*y*(1 - y/1000) - 20, (x, 0, 150), (y, 0, 1200), plot_points = 21)

y