Use Euler's Method with the Specified Step Size to Estimate $y ^ { \prime } = y - e ^ { - 4 x } , y ( 0 ) = 2 , d x = 1 / 3 , x ^ { * } = 2$

question 62

Multiple Choice

Use Euler's method with the specified step size to estimate the value of the solution at the given point x*. Find the value
of the exact solution at x*.
- $y ^ { \prime } = y - e ^ { - 4 x } , y ( 0 ) = 2 , d x = 1 / 3 , x ^ { * } = 2$

• A) Euler's method gives \(y \approx 9.2983\); the exact solution is \(12.9315\)
• B) Euler's method gives \(y \approx 8.2740\); the exact solution is \(11.1513\)
• C) Euler's method gives \(y \approx 9.4866\); the exact solution is \(13.3004\)
• D) Euler's method gives \(y \approx 8.9605\); the exact solution is \(12.3212\)

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