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Simplifying solution of a differential equation

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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))
  4 Comments
Walter Roberson
Walter Roberson on 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.
Aleem Andrew
Aleem Andrew on 14 Jan 2021
That is because there is an additional equation relating k and m, sqrt(k/m) = 2, that I tried to include in the dsolve command to solve the system but got an error message when trying to solve a system of equations, [ode sqrt(k/m) == 2]. Instead the ode = m*Dy2 + k*y == 0; line can be modified to ode = (k/4)*Dy2 + k*y == 0; to obtain the numeric solution.

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Accepted Answer

Walter Roberson
Walter Roberson on 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) = 
ySol(t) = simplify(ySol(t),'steps',500)
ySol(t) = 
pretty(ySol(t))
/ sqrt(43198488722811199054095930230) t \ sqrt(8639697744562239810819186046) sin| ------------------------------------- | 5 / sqrt(43198488722811199054095930230) t \ \ 157178273090335 / cos| ------------------------------------- | + --------------------------------------------------------------------------------- \ 157178273090335 / 274837532398538
vpa(ySol(t), 5)
ans = 

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