Question

Use Euler's method with step size 0.1 to estimate y(1.5), where y(x) is the solution of the initial-value problem y' = 3y + 2xy, y(1) = 1.

Answer 1

Please someone help, I will give 10 medals
.

Answer 2

This problem is due in 10 mintues, please someone help!

Answer 3

what class is this?

Answer 4

Calc 2

Answer 5

you need to construct a table first

Answer 6

http://www.mathscoop.com/calculus/differential-equations/images/euler-table-picture.jpg

Answer 7

Start filling out a table:\[\begin{array}{c|c|c|c|c}
n&x_n&y_n&y'(x_n,y_n)\\
\hline
0&\color{green}1&\color{red}1&3(\color{red}1)+2(\color{green}1)(\color{red}1)=\color{blue}5\\
\hline
1&\color{green}1+0.1=1.1&\color{red}1+\color{blue}5(0.1)=1.5\\
\hline
2&\\
\hline
3&\\
\hline
4&\\
\hline
5&
\end{array}\]

Answer 8

The next step would be
\[\begin{array}{c|c|c|c|c}
n&x_n&y_n&y'(x_n,y_n)\\
\hline
0&1&1&5\\
\hline
1&\color{green}{1.1}&\color{red}{1.5}&2(\color{red}{1.5})+3(\color{green}{1.1})(\color{red}{1.5})=\color{blue}{7.95}\\
\hline
2&\color{green}{1.1}+0.1=1.2&\color{red}{1.5}+\color{blue}{7.95}(0.1)=2.295\\
\hline
3&\\
\hline
4&\\
\hline
5&&&-
\end{array}\]
and so on. Follow the color-coding if you like, but it's better to get an idea of WHY we're doing the calculations we're doing.