Mathematics, 24.03.2020 05:39 mari200150
Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y' = x2y − 1 2 y2, y(0) = 3. (Round your answer to four decimal places.)
Answers: 2
![y(0+0.2)\approx y(0)+0.2[0\times y(0)-\frac12 (y(0))^2]](/tpl/images/0560/6526/1a737.png)
![\Rightarrow y(0.2)\approx 3+0.2[-\frac12 \times3]](/tpl/images/0560/6526/176e8.png)
[∵ y(0) =3 ]
![y(0.2+0.2)\approx y(0.2)+0.2[(0.2)^2\times y(0.2)-\frac12 (y(0.2))^2]](/tpl/images/0560/6526/7e77e.png)
![\Rightarrow y(0.4)\approx 2.7+0.2[(0.2)^2\times 2.7- \frac12(2.7)^2]](/tpl/images/0560/6526/637d2.png)
![y(0.4+0.2)\approx y(0.4)+0.2[(0.4)^2\times y(0.4)-\frac12 (y(0.4))^2]](/tpl/images/0560/6526/aeb1f.png)
![\Rightarrow y(0.6)\approx 1.9926+0.2[(0.4)^2\times 1.9926- \frac12(1.9926)^2]](/tpl/images/0560/6526/1b7cb.png)
![y(0.6+0.2)\approx y(0.6)+0.2[(0.6)^2\times y(0.6)-\frac12 (y(0.6))^2]](/tpl/images/0560/6526/28952.png)
![\Rightarrow y(0.8)\approx 1.6593+0.2[(0.6)^2\times 1.6593- \frac12(1.6593)^2]](/tpl/images/0560/6526/52a5c.png)
![y(0.8+0.2)\approx y(0.8)+0.2[(0.8)^2\times y(0.8)-\frac12 (y(0.8))^2]](/tpl/images/0560/6526/d9970.png)
![\Rightarrow y(1.0)\approx 0.8800+0.2[(0.8)^2\times 0.8800- \frac12(0.8800)^2]](/tpl/images/0560/6526/e1892.png)
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Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-va...
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