symbolic Integration issue while solving differential equation

I am trying to solve differential equation, but i instead of getting explicit solution, i am getting 'int ' expression as shown below. kindly please suggest how i can solve this. Thanks in advance.

yr1=-0.493*exp(-0.1099*t)+0.493*exp(0.0049*t)*cos(1.0005*t); Diffrential equation-> y1(t) = dsolve(10*diff(y1, t, 3)+diff(y1, t, 2)+10*diff(y1, t)+1.1*y1== 0.55*yr1*yr1, y1(0) == 0, Dy1(0) == 0, D2y1(0) == 0);

expression-> int(-(72185553*exp(-(1099*x)/5000)*exp((x*(60*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(1/3) + 900*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(2/3) - 299))/(1800*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(1/3)))*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(2/3)*(exp((287*x)/1250)/2 + (cos((2001*x)/1000)*exp((287*x)/1250))/2 - 2*cos((2001*x)/2000)*exp((287*x)/2500) + 1)*(2700*cos((3^(1/2)*x*(900*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(2/3) + 299))/(1800*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(1/3)))*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(2/3) - 897*cos((3^(1/2)*x*(900*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(2/3) + 299))/(1800*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(1/3))) + 299*3^(1/2)*sin((3^(1/2)*x*(900*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(2/3) + 299))/(1800*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(1/3))) + 900*3^(1/2)*sin((3^(1/2)*x*(900*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(2/3) + 299))/(1800*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(1/3)))*((205957^(1/2)*5400000^(1/2))/5400000 - 259/6750)^(2/3)))/(800*(1390209750*3^(1/2) - 259*3^(1/2)*205957^(1/2)*5400000^(1/2))), x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)

Answer 1

[Torsten]

Seems the solution to your differential equation is given by this integral, but MATLAB is not able to find an analytical expression for this integral. Use a numerical ODE integrator instead (e.g. ODE45).

Best wishes

Torsten

[Santosh Bhagat]

when i put the solution in 'vpa' then vpa changes 'int' in 'numeric::int' with limits. so is there any chance to find the solution through numeric::int, and second how to use this numeric::int in symbolic matlab not in mupad.

Thanks

[Torsten]

so is there any chance to find the solution through numeric::int

If you mean "analytical expression for the solution" by "solution" - then no. If you mean "numerical solution", then yes because vpa gives the numerical solution.

how to use this numeric::int in symbolic matlab not in mupad

You can't use this solution for symbolic computations.

Best wishes

Torsten.