Using dsolve function to solve this equation?
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Question: Use dsolve to solve this equation: y' − y = 2 sin(t).
Below is the code I used but I do not think I am getting the right answer.
syms y(t);
y = dsolve(diff(y) == 2*sin(t)+y)
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Star Strider
il 23 Lug 2016
For grins, I decided to see what a Laplace transform solution would produce:
syms s y(t) y0 Y
Lsin = laplace(sin(t));
Eqn1 = Y*(s-1) == Lsin;
Eqn2 = solve(Eqn1, Y);
Eqn3 = ilaplace(partfrac(Eqn2))
Eqn4 = simplify(Eqn3, 'steps',10)
Eqn3 =
exp(t)/2 - cos(t)/2 - sin(t)/2
Eqn4 =
exp(t)/2 - (2^(1/2)*sin(t + pi/4))/2
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Star Strider
il 23 Lug 2016
My point is that it gives an equivalent answer to the answer dsolve returns when you simplify it. It assumes an initial condition of zero. If you want to specify an initial condition, include one:
syms y(t) y0
y = dsolve(diff(y) == 2*sin(t)+y, y(0) == y0)
y =
exp(t)*(y0 + 1) - 2^(1/2)*cos(t - pi/4)
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