Bernoulli differential equation moving electric car

Hello,

I am trying to plot this function in matlab dv/dt+K*v=-C*v^2 with K and C constants for this particular model.

I know it is a bernoulli equation but I don't know how to solve it exactly.

I am writing

f=@(t,v) -C*v^2-K*v;

[t,v]=ode23(f,[0,20],v0)

plot(t,v)

to evaluate the function between 0 and 20 seconds with an initial speed v0=30 m/s

Thank you

[Star Strider]

C = ?;
K = ?;

[Richard Escriva]

Yes that is defined. I can show the whole code.

ro=1.205; a=2.6; cd=0.34;K=0.05; m=1900; v0=33.333;

C=0.5*ro*a*cd;

f=@(t,v) -C*v^2-K*v;

[t,v]=ode23(f,[0,20],v0);

plot(t,v,'b')

[Ameer Hamza]

Your code seems correct, according to the ODE you posted. Are you getting unexpected results?

[Star Strider]

The plot appears to be essentially a hyperbola.

Were you expecting something else?

[Richard Escriva]

Got it solved, it was a silly mistake I didn't divide the constants by the mass therefore I was having bad results.

Thank you guys.

[Star Strider]

So should it be:

f=@(t,v) -(C/m)*v^2-(K/m)*v;

instead?

[Richard Escriva]

Exactly, you are right. By the way, I am now trying to solve this second order equation:

y''+y+2t=0 / t∈[1,5] / y(1)=y'(1)=2

Is the code correctly written? Thank you

function rk=f(t,y)
    rk=[y(2); -2.*t-y(1)];
end

timerange=[1 5];
initv=[2 2];
[t,y]=ode45(@f, timerange, initv)
plot(t,y(:,1));

[Ameer Hamza]

Yes, the code is correct according to the equation.

[Richard Escriva]

Ok,

thanks bro