Representing and approximating third order differential equations

I am trying to approximate a differential equation in terms of two vectors, x any y and also return a value of a solution. My differential equation is hard to represent though:

d3y/dx3 + dy/dx - xy + d2y/dx2 = 2 xE[1, 5]

initial conditions y(0), dy/dx(0) and d2y/dx2(0) have been given.

Any suggestions?

[Star Strider]

What does ‘2 xE[1, 5]’ mean?

Similar to: http://www.mathworks.com/matlabcentral/answers/124325-how-to-create-diferential-equation-with-initial-conditions.

Answer 1

[Francisco Angel]

Transform the problem in a system of first order differential equations:

dy1 / dx = y2 dy2 / dx = y3 dy3 / dx = 2-y3-x*y1-y2

with initial conditions y1(0) y2(0) and y3(0) then solve it using ode45 for example:

if true
  % code
[t,Y]=ode45(@system,[1 5],[y1(0) y2(0) y3(0)]);
function dy=system(X,Y)
dy(1)=Y(2);
dy(2)=Y(3);
dy(3)=2-Y(3)-X*Y(1)-Y(2);
dy=dy';
end
end
In doubt check formatting issues tipyng help ode45 in command line.