If satisfies the differential equation and , what is the approximate value of , using Euler's method with step size 1?
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We have ( x 0 , y 0 =(0,2)), and then: ( x 1 , y 1 ) ( x 2 , y 2 ) ( x 3 , y 3 ) ( x 4 , y 4 ) = ( 0 + 1 , 2 + 1 ⋅ ( 0 2 + 0 ⋅ 2 ) ) = ( 1 , 2 ) , = ( 1 + 1 , 2 + 1 ⋅ ( 1 2 + 1 ⋅ 2 ) ) = ( 2 , 5 ) , = ( 2 + 1 , 5 + 1 ⋅ ( 2 2 + 2 ⋅ 5 ) ) = ( 3 , 1 9 ) , = ( 3 + 1 , 1 9 + 1 ⋅ ( 3 2 + 3 ⋅ 1 9 ) ) = ( 4 , 8 5 ) ,
so the answer is 85.