Solve expression given definition: find a ratio between symbolic variables

While studying power electronics, in particular the boost converter in DCM mode, you can write some equations.

I can derive the final formula expressing the ratio between the output voltage and the input voltage ( M = U_o/U_i) by hand (and by means, I successfully derived and proved its correctness )

The final result is:

M = 1+D^2 * I_N / I_o

where D is the duty cycle and I_N is..... well you don't have to strictly know it!

It isn't necessary to answer my question!

In fact a set of equations is written (I know them and I understood them) which depend on some parameters, which in turn could be expressed by other parameters.

By hand, I substitute equations within equations, and again and again, I rearrange a bit and then I can solve for the ratio.

I am asking if I can do this tedious (and prone to errors )task within Matlab...

I am using the symbolic variable.

Here is the code it is needed:

syms U_i
syms t_on
syms U_o
syms t_poff
syms I_o
syms I_Lmax
syms Ts
syms fs
syms L  % inductance in Henry
syms I_N
syms D % duty cycle
syms M % ratio between output voltage and input voltage

D = t_on/Ts;
fs = 1/Ts;
I_N = U_i/(2*fs*L);
I_Lmax = U_i * t_on / L;
I_o = I_Lmax*t_poff / (2*Ts);
t_poff = U_i * t_on / (U_o -U_i);
M = U_o / U_i;

I would like to know if there is some magic command or function so that I can type:

result = evidenceAndSolveFor_M_expressing_the_result_in_function_of( 'D', 'I_N', 'I_o' )

>>> M = 1 + D^2 *I_N/I_o

thanks!