solving systems of second order differential equations with initial conditions and plotting

Sorry, I'm completely new to matlab.

I have to solve a system of odes as follows:

x''=-0.003467*x'*((x')^2+(y')^2)^(1/2),

y''=-0.003467*y'*((x')^2+(y')^2)^(1/2)-9.8,

with initial conditions:

x'(0)=160000/3600,

y'(0)=0,

x(0)=0,

y(0)=80,

where x'(t) and y'(t) are the speed in the x direction and y direction,

I have to find what t and x(t) is when y(t)=0, and plot the trajectories.

The anser should be t=4.44s, x(t)=148m.

I tried typing in:

syms x(t) y(t)

S = dsolve(diff(x,2)==-0.003467*diff(x)*((diff(x))^2+(diff(y))^2)^(1/2),diff(y,2)==-0.003467*diff(y)* ((diff(x))^2+(diff(y))^2)^(1/2)-9.8,diff(x(0))==160000/3600,diff(y(0))==0,x(0)==0,y(0)==80)

and what I get was:

Error using mupadengine/feval (line 157)

MuPAD error: Error: The equations are invalid. [ode::new]

Error in dsolve>mupadDsolve (line 328)

T = feval(symengine,'symobj::dsolve',sys,x,options);

Error in dsolve (line 189)

sol = mupadDsolve(args, options);

I know there must be some mistake for I'm completely new to matlab.

Can someone please help me?

Answer 1

[Orion]

Hi,

for ode systems, you don't necessary need to use the symbolic math toolbox, just use basic functions of matlab such as ode45 or ode23