How to use initial conditions with an equation?

Hello I'm wondering how can I use the given initial conditions to an equation e.g. x=0 and y=1 to be used on an equation e.g. Y=2*x^3+6*x^2-10*x+4 and its derivative dydx=6*x^2+12x-10 when I try to plot Y and dydx from 0 to 6 with 0.1 steps. Do I need a for loop or something of that matter?

Answer 1

[Star Strider]

The easiest way is to use polyval:

% Y=2*x^3+6*x^2-10*x+4
% dydx=6*x^2+12x-10

Y = [2  6  -10  4];         % EXPRESS COEFFICIENTS AS A VECTOR
dydx = [6  12  -10];

x = 0:0.1:6;

Y_x = polyval(Y,x);
dydx_x = polyval(dydx,x);

figure(1)
plot(x, Y_x,  x,dydx_x)
grid
legend('Y', '^{dy}/_{dx}', 'Location', 'NW')

Answer 2

[Geoff Hayes]

Luis - no you don't need to use a for loop, but you will have to adjust your equations so that they can compute elementwise operations (i.e. handle vector input rather than just a scalar input).

To do this, any operation that affects your vector must be preceded by a period. Your first equation

 Y=2*x^3+6*x^2-10*x+4

becomes

 Y=2*x.^3+6*x.^2-10*x+4

Note that it was only necessary to precede the exponent operator with a period; all other operations are handled normally.

Then with

 x=0:0.1:6

you can calculate Y with the above equation. You can do the same sort of thing for the derivative.

Note that you mention that your initial conditions are x=0 and y=1. Why is y=1, since if x=0 then your equation evaluates to 4?

Try the above and see what happens!