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Using dsolve function to solve this equation?

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Bob
Bob 2016-7-23
评论： Star Strider 2016-7-23
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
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
Bob 2016-7-23
I need to use the dsolve function, so this does not help me at all.
Star Strider
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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