MATLAB: Simultaneous equation using sym x y

simultaneous equationtrigonometry

I have a simultaneous equation involving angles, I searched the example code given in the Matlab website and got to know this function,

syms x y 
eqn1 = (x*cosd(90-declin(star_1))) + (y*sind(90-declin(star_1))*cosd(180-hour_angle1))  == sind(altitude1);
eqn2 = (x*cosd(90-declin(star_2))) + (y*sind(90-declin(star_2))*cosd(180-hour_angle2))  == sind(altitude2);
sol = solve([eqn1, eqn2], [x, y]);
xSol = sol.x;
ySol = sol.y;

however the result of xSol and ySol returns me are in the equation as follow:

 xSol =8574394107518575345582913247962335860353333952/363377113639125604827290236669541719008437000669

and whatever mathematical operation I use on xSol or ySol gives me similar answers, are there any way for me to obtain the numerical value of the equation? I have tried using abs(xSol) to obtain the magnitude, but the result is still the same. Any help would be appreciated =)

I am running on MatlabR2017b.

Best Answer

double(xSol)

or in the case of expressions that still have a symbolic variable in them,

vpa(xSol)

Related Solutions

MATLAB: Solve differential equation using ode23 and ode45

Firstly, as correctly mentioned in the comments, the eqn variable should be written as-

eqn = diff(x, y) == (x + y*exp(y));

Now, for plotting the solution, you can use fplot- fplot documentation

xSol = simplify(dsolve(eqn, cond)); %simplify, as the name suggests, simplifies the expression obtained after dsolve
fplot(xSol);

Now, about using ode23 or ode45, I suggest you to refer to the documentation to gain an understanding on the same. I am posting a code below which uses ode45 (referred directly from the documentation)-

[y, x] = ode45(@(y, x) (x + y*exp(y)), [-10 10], 1)

Link to ode45 documentation- ODE45

MATLAB: Solving Diophantine Equations in MATLAB

Use the “solve” function. Before using “solve”, assume that the variables in the Diophantine equation are integers to ensure “solve” returns integer solutions. For example, solve the linear Diophantine equation 1027*x + 712*y = 1;

For MATLAB R2015a and later:

syms x y integer                % assume ‘x’ and ‘y’ are integers

eqn = 1027*x + 712*y == 1;       % declare the equation

[xSol, ySol] = solve(eqn,[x y])  % solve for ‘x’ and ‘y’

xSol =
-165
ySol =
238

For MATLAB R2014b or before:

syms x y
assume([x y], 'integer')        % assume ‘x’ and ‘y’ are integers
eqn = 1027*x + 712*y == 1;       % declare the equation
[xSol, ySol] = solve(eqn,[x y])  % solve for ‘x’ and ‘y’
xSol =
-165
ySol =
238

For details on “solve”, see: https://www.mathworks.com/help/symbolic/solve.html

For more information on assumptions, see: https://www.mathworks.com/help/symbolic/assumptions-for-symbolic-objects.html

Best Answer

Related Solutions

MATLAB: Solve differential equation using ode23 and ode45

MATLAB: Solving Diophantine Equations in MATLAB

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