Use Euler's method with n = 5 to approximate f(1) if y = f(t) satisfies the differential equation $y ^ { \prime } = y$ $y ( 0 ) = 1$ Compare this answer with the exact value of f(1). Is the following the correct answer?
Euler's method: f(1) ≈ 2.488; Actual value: f(t) = e ≈ 2.718

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Quizplus · Accepted Answer

Euler's method is a numerical technique to approximate solutions of differential equations. Given $y' = y$ with $y(0) = 1$, and using $n = 5$ steps to approximate $f(1)$, the result is indeed close to 2.488. The exact solution of the differential equation is $f(t) = e^t$, so the actual value of $f(1)$ is $e \approx 2.718$. The approximation and the actual value provided match the expected outcomes of applying Euler's method and the exact solution, respectively.

Use Euler's Method with N = 5 to Approximate F(1) y′=yy ^ { \prime } = yy′=y

Use Euler's Method with N = 5 to Approximate F(1) $y ^ { \prime } = y$