1. Consider the initial value problem y′ = −5xy, y(0) = 5 .
(a) Use Euler’s Method to estimate y(1) to 4 decimal places, with 10 steps. (b) What is the true solution of the initial value problem ?

for a) I got y(1) = 0.3273
how do I solve for b) what does it mean by true solution of the initial value?

Please don't give me the answer directly.

Question

1. Consider the initial value problem y′ = −5xy, y(0) = 5 .
(a) Use Euler’s Method to estimate y(1) to 4 decimal places, with 10 steps. (b) What is the true solution of the initial value problem ?

for a) I got y(1) = 0.3273
how do I solve for b) what does it mean by true solution of the initial value?

Please don't give me the answer directly.

australopithecus · Answer

I found a resource that talks about finding the true solution but I have no idea where they got

y = 0.25e^(2x) - 0.5x - 0.25 from y = x + 2y

australopithecus · Answer

link here: http://calculuslab.deltacollege.edu/ODE/7-C-1/7-C-1-h-c.html

australopithecus · Answer

There are also the questions

(c) What is the true value of y(1) to 4 decimal places ?
(d) What is the error of the approximation in (a) ?

Which I have no idea how to solve

anonymous · Answer

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