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Solving Systems of ODE’s Dr. Mohammed Alsayed

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Again we need the dsolve function. Example: For the system y 1 ' = y 2, y 2 ' = -y 1 + sin(5 t) with the initial conditions y 1 (0) = 1 y 2 (0) = 0

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Solution type sol = dsolve('Dy1=y2','Dy2=-y1+sin(5*t)','y1(0)=1','y2(0)=0','t') sol = y1: [1x1 sym] y2: [1x1 sym]

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sol.y1 Gives -2/3*sin(t)*cos(t)^4+1/2*sin(t)*cos(t)^2+1/6*sin(t)+cos(t). This can be simplified by typing s1 = simple(sol.y1) which gives -1/24*sin(5*t)+5/24*sin(t)+cos(t). For the second component y2 of the solution we proceed in the same way: Typing s2 = simple(sol.y2) gives -sin(t)-5/24*cos(5*t)+5/24*cos(t). To plot the solution curves use ezplot: ezplot(sol.y1, [0,20]) hold on ezplot(sol.y2, [0,20]) hold off

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Polar Differentiation. Let r = f( θ ) and ( x,y) is the rectangular representation of the point having the polar representation ( r, θ ) Then x = f( θ.

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