direction field and solution curve for differential equation.

given function dy/dt = -ty^3

the solution of function is +-1/sqrt(t^2+C) and y(0) = +-1/sqrt(c).

I cannot deal with this solution with C

How can I find solution curves for the differential equation and combined graph of solution curve with direction field.

For solution curve, I used

syms y(t) c

sol = dsolve(diff(y, t) == -t*y^3, y(0) == [-1 1]/sqrt(c))

fplot (sol, [-3, 3])

For direction field

[T, Y] = meshgrid(-2:0.2:3, -1:0.2:2);

S = -t*y^3;

L = sqrt(1 + S.^2) <- I don't know what that means actually

quiver(T, Y, 1./L, S./L, 0.5) axis equal tight

Please help me!

Answer 1

[esat gulhan]

Maybe like this

if it works please accept the answer

clc; clear;
syms y(t) c
sol =  diff(y, t) == -t*y^3 %your equation
cond=y(0) == 1/sqrt(c); %condition for 1/sqrt(c)
sol2=(dsolve(sol,cond));%solution of differential in cond
cond2=y(0) == -1/sqrt(c);%condition for -1/sqrt(c)
sol3=(dsolve(sol,cond2));%solution of differential in cond2
for c=linspace(0.25,10,8); %c values for condition, i take it free, you can change it
t=linspace(-3,3,100);%t values in -3 3 with 100 divides
plot(t,subs(sol2),'b','LineWidth',1.5); %plot lines with cond 1
hold on
plot(t,subs(sol3),'b','LineWidth',1.5);grid on;%plot lines with cond 2
end
[t, y] = meshgrid(-3:0.2:3, -2:0.2:2);%limits of meshgrid
S = -t.*y.^3; 
L = sqrt(1 + S.^2)
quiver(t, y, 1./L, S./L, 0.5) 
set(gca, 'XLim', [-3 3], 'YLim', [-2 2]);%limits of graph

[Hyun Suk Song]

Actually they give me this

Error using plot

Data must be numeric, datetime, duration or an array convertible to double.

Error in projectB (line 34)

plot(t, subs(sol2), 'b', 'LineWidth',1.5);

I don't know why this code is not working

Answer 2

[esat gulhan]

Did you copy to code in a new blank script. It is not an extension of a code it is a new indepentend code. It must work. Impossıble not to work. plot(t, subs(sol2), 'b', 'LineWidth',1.5); can not be in line 34 in ,it is in line 12.

Plot will seen like this