# Solve nonlinear 2nd order ODE numerically

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Lucas on 28 Jul 2022
Commented: MOSLI KARIM on 12 Aug 2022
I need to solve the following nonlinear 2nd order ODE, that is, find such that 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 CommentsShowHide 1 older comment
Lucas on 29 Jul 2022
My idea was to screen these conditions to find one that satisfies my problem.

Sam Chak on 28 Jul 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
##### 1 CommentShowHide None
Lucas on 29 Jul 2022
That worked, thanks!

### More Answers (2)

James Tursa on 28 Jul 2022

MOSLI KARIM on 12 Aug 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
##### 1 CommentShowHide None
MOSLI KARIM on 12 Aug 2022
you can used this code for solved your problem

R2018a

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