ODE45 needs column vector from anonymous function

I am trying to be able to use this code to plot the solution to this differential equation with 4 initial conditions and eventually have a legend with labels for each line plotted.

So far I have the code and output:

options = odeset('RelTol',1e-4,'AbsTol',1e-2);
yprime = @(x,y) ((-x.*y)/(sqrt(6-(y.^2))));
y0 = [0.5 1.0 1.5 2.0];
tspan = [0 5];
[x,y] = ode45(yprime,tspan,y0);
plot(t,y)
grid on
xlabel('x')
ylabel('y')
legend('0.5','1.0','1.5','2.0')

Error using odearguments

@(X,Y)((-X.*Y)/(SQRT(6-(Y.^2)))) must return a column vector.

Error in ode45 (line 107)

odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

I tried adding yprime = yprime'; after line 2 to make the output into a column vector, but that gave the error: Unary operator ''' is not supported for operand of type 'function_handle'.

Any help is appreciated!

Answer 1

[Star Strider]

Do element-wise division:

yprime = @(x,y) ((-x.*y)./(sqrt(6-(y.^2))));

↑

and it does —

options = odeset('RelTol',1e-4,'AbsTol',1e-2);
yprime = @(x,y) ((-x.*y)./(sqrt(6-(y.^2))));
y0 = [0.5 1.0 1.5 2.0];
tspan = [0 5];
[t,y] = ode45(yprime,tspan,y0);
plot(t,y)
grid on
xlabel('x')
ylabel('y')
legend('0.5','1.0','1.5','2.0')

.

Answer 2

[KSSV]

options = odeset('RelTol',1e-4,'AbsTol',1e-2);
yprime = @(x,y) ((-x.*y)/(sqrt(6-(y.^2))));
Y = [0.5 1.0 1.5 2.0];

tspan = [0 5];
y = cell(length(Y),1) ;
figure
hold on
for i = 1:length(Y)
    y0 = Y(i) ;
    [x,y{i}] = ode45(yprime,tspan,y0);
    plot(x,y{i}) ; 
end
grid on
xlabel('x')
ylabel('y')
legend('0.5','1.0','1.5','2.0')