how can i fix this error

clc;

clear all

dsolve('Dy = (10/3)*((x)*(y.^(2/5)))', 'y(0)=1')

Error using symengine

Invalid input. Expected 'expression'.

Error in mupadengine/evalin (line 132)

res = mupadmex(statement,output_type{:});

Error in dsolve>mupadDsolve (line 336)

sys = [sys_sym reshape(evalin(symengine, sys_str), 1, [])];

Error in dsolve (line 194)

sol = mupadDsolve(args, options);

Error in Untitled (line 5)

dsolve('Dy = (10/3)*((x)*(y.^(2/5)))', 'y(0)=1')

Answer 1

[Star Strider]

I have no idea if ‘x’ is a variable or a function, so I am assuming that it is a variable here.

The correct expression would be:

syms x y(t) t Y 
Dy = diff(y);
dsolve(Dy == (10/3)*((x)*(y.^(2/5))), y(0)==1)

however there is no analytic expression for ‘y’, so dsolve (with the corrected version of that expression) returns:

ans =  
((3*int((10*x(x))/3, x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))/5 + 1)^(5/3)

A numeric integration will require the function to be in a form that the ODE solvers can use:

[VF,Subs] = odeToVectorField(Dy == (10/3)*((x)*(y.^(2/5))));
yodefcn = matlabFunction(VF, 'Vars',{t,Y,x})

that would then be passed (for example to ode45) as:

tspan = [ ];
x = ...;
[t,y] = ode45(@(t,y)yodefcn(t,y,x), tspan, 1);

Or something similar.