Module 1 MATLAB Homework

1. Sketch, using MATLAB, the slope field and then draw some solution curves for

dydx=x-y

Interpret your solution curves; that is, describe the behavior of the function f(x, y).

dydx=y-sinx

Interpret your solution curves; that is, describe the behavior of the function f(x, y).

2. Use MATLAB to find the general real solution to of the differential equation

dydx=cosxy2

I need help getting the solution curves into my MATLAB code.... Please help?

%given example %figure(2); %[T,Y]=meshgrid(-2:0.2:3,-1:0.2:2); %S=Y-Y.^2; %L=sqrt(1+S.^2); %quiver(T,Y,1./L,S./L,0.5),axis equal tight %xlabel 't', ylabel 'y' %title 'Direction Field for dy/dt=y-y^2'

%Problem 1a Sketch, using MATLAB, the slope field %and then draw some solution curves for dy/dx= x-y figure(1) [X,Y]=meshgrid(-2:0.2:3,-1:0.2:2); S=X-Y; L=sqrt(1+S.^2); quiver(X,Y,1./L,S./L,0.5),axis equal tight xlabel 'x', ylabel 'y' title 'Direction Field for dx/dy=x-y' ; %Problem 1b Sketch, using MATLAB, the slope field %and then draw some solution curves for dy/dx= y-sin(x) figure(2) [X,Y]=meshgrid(-2:0.2:3,-1:0.2:2); S=Y-sin(X); L=sqrt(1+S.^2); quiver(X,Y,1./L,S./L,0.5),axis equal tight xlabel 'x', ylabel 'y' title 'Direction Field for dy/dx=y-sinx' ; %Solve Given Differential Equation syms y(x) eqn=diff(y,x)==cos(x)/y^2; ySol(x)=dsolve(eqn); fprintf('The general solution for dy/dx= cos(x)/y^2 is y(x)= ') disp(ySol(x)) ;