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)
采纳的回答
Star Strider
2016-7-23
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
2 个评论
Bob
2016-7-23
Star Strider
2016-7-23
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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