Simplifying solution of a differential equation

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))

[Walter Roberson]

Undefined variables k, m

[Aleem Andrew]

I have edited the post. m and k are symbolic variables

[Walter Roberson]

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]

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.

Answer 1

[Walter Roberson]

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 = 

[Aleem Andrew]

Thank you for your answer