how to create direction field for ode?

Question

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hi there

my equation is: x^2*(dy/dx)+ x*y =1;

i want to draw the direction field of first-order linear ODE

the code for direction field is:

------------------------------------

clear;
dist1=linspace(-10,10,80);
[x,y]=meshgrid(dist1);
dydx=((1-x.*y)./x^2);
v=sqrt(1+dydx^2);
quiver(x,y,1./v,dydx./v,'m');

result is dummy :

----------------------------------but when i solve the eqn :y= (log(x)+c1)./x

and with plot command i draw these graphs.

question:how coud i produce direction field which is compatible with graphs and where is the code mistake?

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Sai Ram Charan 2021-2-20

Hope this helps

Answer 1

sam shafi 2021-8-23

0 个投票

syms y(t)

ode = diff(y)+4*y == exp(-t);

cond = y(0) == 1;

ySol(t) = dsolve(ode,cond)