 Sketch the vector fields for each value of the parameter; indicate equilibria and their stability:
 \[
x’=3\sin(x)+x+a, a=3,0,3;
\]  \[
x’=\tan(x)3x+a, a=5,0,5;
\]  \[
x’=e^xx+a, a=1,0,1;
\]
 \[
 Find the three consecutive Picard iterations for the equation.
Solve the differential equation; compare the Taylor expansion of the result with the third Picard iteration. \[
y’=y+1, y(0)=0.
\]  \[
y’=y^2+1, y(0)=0.
\]  \[
y’=y(1y), y(0)=1/2.
\]
 \[

Solve:
 \[
xy”’=y”xy”;
\]  \[
yy”+y=(y’)^2;
\]  \[
yy”’+3y’y”=0.
\]
 \[
september 19
Leave a Reply Click here to cancel reply.
You must be logged in to post a comment.
No comments yet.