draw othorgonal trajectories using differential equations

to draw orthogonal trajectories am i suppose to use dfield or is ezplot as shown below on the right track

Using the Matlab draw the families of orthogonal trajectories for the following differential equation 1) dy /dx = a*x*y /(b*x^2−c*y^2 )

2) dy/ dx = −d*x /e*y

syms y(x) x y

ode = diff(y,x) == (a*x*y)/(b*x^2-c*y^2);

ysol(x) = dsolve(ode)

ezplot(y(x))

error coming up

Answer 1

[madhan ravi]

Not more than two variables have to be symbolic so a,b,c valyes are assigned:

syms y(x) 
a=2;
b=3;
c=5;
ode = diff(y,x) == (a*x*y)/(b*x^2-c*y^2);
ysol = vpa(dsolve(ode));
ezplot(ysol(1))
hold on
ezplot(ysol(2))
ezplot(ysol(3))

[Brenda Galabe]

for second diff equation

syms y(x)

a=2;

b=3;

c=5;

d= 5;

e = 8;

ode = diff(y,x) == (-d*x)/(e*y);

ysol = vpa(dsolve(ode));

ezplot(ysol(1))

hold on

ezplot(ysol(2))

ezplot(ysol(3))

getting this error

index exceeds matrix dimensions.

Error in sym/subsref (line 776)

R_tilde = builtin('subsref',L_tilde,Idx);

Answer 2

[Brenda Galabe]

thats for the first one correct ? do the same for the second. it worked great thanks

also when i get this error what does it mean

Warning: Explicit solution could not be found;

implicit solution returned.

> In dsolve (line 208)

[madhan ravi]

It means the equation cannot be solved

[Brenda Galabe]

ok thank you. awesome do you tutor at all ? great knowledge on matlab. thanks

[madhan ravi]

Anytime :) , no I don't tutor anyone.

[Brenda Galabe]

FOR THE SECOND EQUATION KEEP GETTING AN EMPTY PLOT

ode = diff(y,x) == (-d*x)/(e*y);
ysol = vpa(dsolve(ode))
ysol =subs(ysol,'C2',25)
fplot(ysol(1))
hold on
fplot(ysol(2))

[madhan ravi]

syms y(x) C5  %C5 arises in ysol change it to your constant whether C2 or etc.. doesn't matter
d= 5;
e = 8;
dydx=diff(y);
ode = dydx == (-d*x)/(e*y);
ysol = vpa(dsolve(ode));
y1=subs(ysol,C5,4);
fplot({y1(1),y1(2)})