Question

1. Consider the ODE y'(t) = 1 - t + 4y with initial condition y(0) = 1. (a) Show that the solution is y(t) = 1/4 t - 3/16 + 19/16 e^(4t). (b) Use Matlab to approximate this solution for 0 <= t <= 2 using Euler's method with delta t = 0.05, 0.025, 0.01, and 0.001. Plot your results and the exact solution on the same set of axes in the t - y plane. Fill in the following tables solutions t | approx delta t = 0.05 | approx delta t = 0.025 | approx delta t = 0.01 | approx delta t = 0.001 | exact y(t) 0 | 1 | 1 | 1 | 1 | 1 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 1.0 | 1.5 | 2.0 | error t | delta t = 0.05 | delta t = 0.025 | delta t = 0.01 | delta t = 0.001 0 | 0 | 0 | 0 | 0 0.5 | 1.0 | 1.5 | 2.0 |

          1. Consider the ODE y'(t) = 1 - t + 4y with initial condition y(0) = 1.
(a) Show that the solution is y(t) = 1/4 t - 3/16 + 19/16 e^(4t).
(b) Use Matlab to approximate this solution for 0 <= t <= 2 using Euler's method with delta t = 0.05, 0.025, 0.01, and 0.001. Plot your results and the exact solution on the same set of axes in the t - y plane. Fill in the following tables
solutions
t | approx delta t = 0.05 | approx delta t = 0.025 | approx delta t = 0.01 | approx delta t = 0.001 | exact y(t)
0 | 1 | 1 | 1 | 1 | 1
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
1.0 |
1.5 |
2.0 |
error
t | delta t = 0.05 | delta t = 0.025 | delta t = 0.01 | delta t = 0.001
0 | 0 | 0 | 0 | 0
0.5 |
1.0 |
1.5 |
2.0 |

1. Consider the ODE y'(t) = 1 - t + 4y with initial condition y(0) = 1.
(a) Show that the solution is y(t) = 1/4 t - 3/16 + 19/16 e^(4t).
(b) Use Matlab to approximate this solution for 0 <= t <= 2 using Euler's method with delta t = 0.05, 0.025, 0.01, and 0.001. Plot your results and the exact solution on the same set of axes in the t - y plane. Fill in the following tables
solutions
t | approx delta t = 0.05 | approx delta t = 0.025 | approx delta t = 0.01 | approx delta t = 0.001 | exact y(t)
0 | 1 | 1 | 1 | 1 | 1
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
1.0 |
1.5 |
2.0 |
error
t | delta t = 0.05 | delta t = 0.025 | delta t = 0.01 | delta t = 0.001
0 | 0 | 0 | 0 | 0
0.5 |
1.0 |
1.5 |
2.0 |

Added by Wesley G.

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