MATLAB: How to lapace results

differential equationsMATLAB

how to plot this please

deqdiff = 'diff(y(t),t,t) + y(t) - cos(t)'
ldeqdiff = laplace(deqdiff,t,s)
sldeqdiff = subs(ldeqdiff,{'D(y)(0)','y(0)'},{1,1})
syms Ys
ldeqinit = subs(sldeqdiff,'laplace(y(t),t,s)',Ys)
ly = solve(ldeqinit,Ys)
ilaplace(ly,s,t)

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syms s t y(t)
Dy = diff(y);
deqdiff = diff(y(t),t,t) + y(t) - cos(t);
ldeqdiff = laplace(deqdiff,t,s);
sldeqdiff = subs(ldeqdiff,{Dy(0), y(0)},{1,1});
syms Ys
Lyt = laplace(y(t), t, s);
ldeqinit = subs(sldeqdiff, Lyt, Ys);
ly = solve(ldeqinit,Ys);
ily = ilaplace(ly,s,t);
fplot(ily, [0 20])

Related Solutions

MATLAB: Solving second order differential equations with LaPlace Transforms: getting an error when trying to input an initial condition (R2017b) (“error: untitled line”)

The laplace function does not accept initial conditions (as dsolve does).

I requested this as an enhancement several months ago. It has thus far not appeared.

You will have to do coding gymnastics with the subs function to do the necessary substitutions.

MATLAB: Matlab Symbolic Maths – How to insert ¨y(t) +˙y(t) +y(t)= f(t) equation in symbolic Maths

Although there are easier ways to solve this equation in MATLAB (e.g., using dsolve()), you mentioned Laplace transform in your question. The following code shows how to use it Laplace, and inverse Laplace transform to find the impulse response.

syms y(t) f(t) Ly
dy = diff(y, 1);
ddy = diff(y, 2);
ic = [0 0]; % initial condition: y(0)=0, y'(0)=0
eq = ddy + dy + y == f; % differential equation
eq_impulse = subs(eq, f(t), dirac(t)); % substitude f(t)=dirac(t) i.e., impulse input
eq_laplace = laplace(eq_impulse); % laplace transform of equation
eq_laplace = subs(eq_laplace, [y(0) dy(0) laplace(y)], [ic Ly]); % substituting initial conditions
Ly = solve(eq_laplace, Ly); % seperating the laplace(y) term
y(t) = ilaplace(Ly); % inverse laplace transform
fplot(y, [0 10]); % plot from t=0 to t=10

Best Answer

Related Solutions

MATLAB: Solving second order differential equations with LaPlace Transforms: getting an error when trying to input an initial condition (R2017b) (“error: untitled line”)

MATLAB: Matlab Symbolic Maths – How to insert ¨y(t) +˙y(t) +y(t)= f(t) equation in symbolic Maths

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