Question

please solve with mathlab and post screenshots of the code

Circle your final answer. 2. y" +16y 8 cos(4t) y(o)-y'(O)- 2.У

Answer 1

syms y(t)
Dy = diff(y);

ode = diff(y,t,2)-6*diff(y,t)+9*y == t*exp(3*t);
cond1 = y(0) == 0;
cond2 = Dy(0) == 5;
conds = [cond1 cond2];
ySol(t) = dsolve(ode,conds)

ySol(t) = 5*t*exp(3*t) + (t^3*exp(3*t))/6

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syms y(t)
Dy = diff(y);

ode = diff(y,t,2)+16*y == 8*cos(4*t);
cond1 = y(0) == 0;
cond2 = Dy(0) == 0;
conds = [cond1 cond2];
ySol(t) = dsolve(ode,conds)

ySol(t) = cos(12*t)/16 - cos(4*t)/16 + sin(4*t)*(t + sin(8*t)/8)

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syms y(t)
Dy = diff(y);

ode = diff(y,t,2)-4*diff(y,t)+4*y == 6*exp(2*t);
cond1 = y(0) == 0;
cond2 = Dy(0) == 0;
conds = [cond1 cond2];
ySol(t) = dsolve(ode,conds)

ySol(t) = 3*t^2*exp(2*t)

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syms y(t)
Dy = diff(y);

ode = diff(y,t,2)-4*diff(y,t) == -4*t*exp(2*t);
cond1 = y(0) == 0;
cond2 = Dy(0) == 1;
conds = [cond1 cond2];
ySol(t) = dsolve(ode,conds)

ySol(t) = t*exp(2*t)