Simplifying solution of a differential equation
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Aleem Andrew
am 14 Jan. 2021
Kommentiert: Aleem Andrew
am 14 Jan. 2021
The most simplified version of ySol(t), the solution to the differential equation below, is 1.5*sin(2t+0.7297), but the output of the following code is in terms of exponential functions. Can someone explain how the output can be further simplified?
syms y(t) m k
Dy = diff(y,t); Dy2 = diff(y,t,2);
ode = m*Dy2 + k*y == 0;
cond = [y(0) == 1,Dy(0) == sqrt(5)];
ySol(t) = dsolve(ode,cond)
ySol(t) = simplify(ySol(t),'steps',500)
pretty(ySol(t))
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Walter Roberson
am 14 Jan. 2021
When m and k are symbolic, you get symbolic expressions for the coefficients, not numeric ones like you show as your desired output.
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Walter Roberson
am 14 Jan. 2021
m = rand(); k = rand();
syms y(t)
Dy = diff(y,t);
Dy2 = diff(y,t,2);
ode = m*Dy2 + k*y == 0;
cond = [y(0) == 1,Dy(0) == sqrt(5)];
ySol(t) = dsolve(ode,cond)
ySol(t) = simplify(ySol(t),'steps',500)
pretty(ySol(t))
vpa(ySol(t), 5)
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