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ProblemSetE - Problem Set E%Do problems 12,13abc,17acd,18...

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%% Problem Set E % %Do problems 12,13abc,17acd,18 from the Problem Set E in DEwM pp193-205 %Note: the equation in 12b) shoud read y''+2y'+2y=0 and in 13a) h(t) should %be 1 on pi<=t<10 and 0 otherwise. % ode12a = 'D2y + 2*Dy + 2*y = sin(t)'; sol12a = dsolve(ode12a, 'y(0) = 0' , 'Dy(0) = 0') ezplot(sol12a , [0 pi]); title 'Graph of solution for D2y + 2*Dy + 2*y = sin(t) on interval 0 to pi'; %b - to find the numerical values for y(pi) and y'(pi) I used the %substitution method to sub in pi for the solution to part and and into the %derivative for the solution for part a ypi = subs(sol12a , t , pi); Dy = diff(sol12a); Dypi = subs(Dy, t, pi); ode12b = 'D2y + 2*Dy + 2*y = 0'; %solution of the differential equation with the new initial condidtions sol12b = dsolve(ode12b , 'y(pi) = 0.3827', 'Dy(pi) = -0.1914') ezplot(sol12b , [pi 15]); title 'D2y + 2*Dy + 2*y = 0 with the initial conditions y(pi) = 0.3827 Dy(pi) = -0.1914' figure hold on ezplot(sol12a, [0 pi]); ezplot(sol12b, [0 15]); title 'solution to D2y + 2*Dy + 2*y = 0 on interval 0<t<15' %% C Solving the Equation Using the Laplace Transform Method syms s t Y % first define the variables eqn = sym('D(D(y))(t) + 2*D(y)(t)+2*y(t) = heaviside(t)*sin(t) + heaviside(t-pi)*(- sin(t))');% defining the differential equation
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