Solve nonlinear 2nd order ODE numerically

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Lucas
Lucas el 28 de Jul. de 2022
Comentada: MOSLI KARIM el 12 de Ag. de 2022
I need to solve the following nonlinear 2nd order ODE, that is, find such that
1-x=-\frac{y''(x)}{(1+(y'(x))^2)^{{3/2}}
I tried using
>> syms y(x)
>> ode = -diff(y,x,2)/(1+(diff(y,x))^2)^(3/2) == 1-x;
>> ySol(x) = dsolve(ode)
but it doesn't work since apparently there is no anaylitical solution (if I rearrange the terms it does find a system of complex solutions, but I think the it is not right).
Isn't there a command to solve ODEs numerically? I am expeting something like the family of plots from here https://www.wolframalpha.com/input?i=f%27%27%28t%29%2F%28%281%2B%28f%27%28t%29%29%5E2%29%5E%283%2F2%29%29+%3D+-%281-0.25t%29
Many thanks oin advance!
  2 comentarios
Torsten
Torsten el 28 de Jul. de 2022
What are your initial/boundary conditions for y ?
Lucas
Lucas el 29 de Jul. de 2022
My idea was to screen these conditions to find one that satisfies my problem.

Iniciar sesión para comentar.

Respuesta aceptada

Sam Chak
Sam Chak el 28 de Jul. de 2022
You can follow the example here
and try something like this:
tspan = [0 1.15];
y0 = [1 0]; % initial condition
[t,y] = ode45(@(t, y) odefcn(t, y), tspan, y0);
plot(t, y(:,1)), grid on, xlabel('t')
function dydt = odefcn(t, y)
dydt = zeros(2,1);
c = 0.25;
dydt(1) = y(2);
dydt(2) = - (1 - c*t)*(1 + y(2)^2)^(3/2);
end

Más respuestas (2)

James Tursa
James Tursa el 28 de Jul. de 2022

MOSLI KARIM
MOSLI KARIM el 12 de Ag. de 2022
function pvb_pr13
tspan=[0 1.5];
y0=[1 0];
[x,y]=ode45(@fct,tspan,y0);
figure(1)
hold on
plot(x,y(:,1),'r-')
grid on
function yp=fct(x,y)
c=0.25;
yp=[y(2);-(1-c*x)*((1+(y(2))^2)^(3/2))];
end
end

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