@Carl Love 

Ou! I understand. Thank you for a detailed answer and advices! I'll try to finish my problem and I do it.

If you want you can look at my code but it's bulky.

soluTest_2.mw

@Preben Alsholm 

I'm sorry. I didn't see the dsolve.

Yes, of course dsolve is a good solver but I need to go by my way through my solution and I need to verify my solution.

Thank you for your help!

@Preben Alsholm 

Yes! I run your code and obtain {0} from odetest. I think we obtain zero because solution solODE aren't specified. In this code we do not set W1, gamma1, Wb1, gammab1 - they are void. This void satisfy equations sysODE and we obtain zero.

I would like to thank you for your help.

@Carl Love

Thank you for the answer!

I have refined my question bellow. Please look it.

@Preben Alsholm 

Thank you for your answer!

I'll try to refine my question. Initial values aren't given. The system of equations has a form:

> ode1 := diff(W1(x),[x$2])+diff(gamma1(x),x)-2*g^2*W1(x) = 0;
> ode2 := diff(gamma1(x),[x$2])-b*gamma1(x)-b*(diff(W1(x),x)) = 0;
> ode3 := diff(Wb1(x), [x$2])+diff(gammab1(x),x)-2*gb^2*Wb1(x) = 0;
> ode4 := diff(gammab1(x),[x$2)])-bb*gammab1(x)-bb*diff(Wb1(x),x) = 0;
> 
> sysODE := {ode1, ode2, ode3, ode4}, {W1, Wb1, gamma1, gammab1}(x);

But I think the form of equations is not significant for my question. I have solution for this system obtained by myself without dsolve. And I wanna check my solution. I have expression for the function W1, Wb1, gamma1, gammab1 like

W1 = F1(x,d1,...,d8,g,gb,b,bb,....) 
Wb1 = F2(x,d1,...,d8,g,gb,b,bb,....) 
gamma1 = F3(x,d1,...,d8,g,gb,b,bb,....)
gammab1 = F4(x,d1,...,d8,g,gb,b,bb,....) 

where F1,..F4 - some functions from x; d1,..d8 - integration constants; g,gb,b,bb - parameters from equations; and from another parameters.

Set of the solution is:

> solODE:={W1(x)=..., Wb1(x)=...,gamma1(x)=...,gammab1(x)=...}

And I use odetest to verify this solution.

> odetest(solsysODE, sysODE)

If I right understand odetest gives me misalignment between solution and equation. If it gives me {0} - it's Ok, if - {some expression} - it's bad. But in my case odetest gives me

> {0, expression, expression}

The question is - what does it mean? Why do I obtain set from three values? Why the set has three values not one or four (respective to number of equations)? What each values means?

Please, could you answer me these questions?

Thank you.