Solve a nonlinear ODE (first order) and optimize it in order to find the unknown parameters

It is needed a to solve a nonlinear ODE (first order) with ode45 solver in Matlab and then to optimize it to find 3 unknown parameters with cost function. The system of the ODE is simulated in separated software and 4 inputs to the ODE equation are provided. These 4 inputs (sets of data-temperatures) are taken out of the [login to view URL] have to solve the nonlinear ODE with these sets of data and with three unknown parameters(U0,U,n). After that with the use of the cost function find these unknown parameters. The ODE equation and the inputs to it are provided in the attachements. The solution matlab files with the function must be provided.