Use Euler's Method to Calculate the First Three Approximations to the Given

question 63

Multiple Choice

Use Euler's method to calculate the first three approximations to the given initial value problem for the specified increment size. Round your results to four decimal places.
- $y ^ { \prime } = y ^ { 2 } ( 1 - 2 x ) , y ( - 1 ) = - 1 , d x = 0.5$

• A) \(\mathrm { y } _ { 1 } = 0.4 , \mathrm { y } _ { 2 } = 0.63 , \mathrm { y } _ { 3 } = 0.7472\)
• B) \(\mathrm { y } _ { 1 } = 0.7 , \mathrm { y } _ { 2 } = 0.99 , \mathrm { y } _ { 3 } = 1.9136\)
• C) \(\mathrm { y } _ { 1 } = 0.5 , \mathrm { y } _ { 2 } = 0.75 , \mathrm { y } _ { 3 } = 1.03125\)
• D) \(\mathrm { y } _ { 1 } = 0.7 , \mathrm { y } _ { 2 } = 0.99 , \mathrm { y } _ { 3 } = 1.2656\)

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