how to solve set of differential equation Warning: Unable to find explicit solution. > In dsolve (line 190)

syms A1(z) A2(z) 
n1=1;
n2=1;
L=100;
deltak=2*pi/L;
ode1 = diff(A1) == i*n1*A1*A2*exp(-i*deltak*z);
ode2 = diff(A2) == i*n2*A1^2*exp(i*deltak*z);
cond1=A(0)==1
cond2=A(1)==0
dsolve([ode1,ode2],[cond1,cond2])

[Walter Roberson]

A is not defined in your boundary conditions. Probably A(0) should be A1(0) and A(1) should be A2(0) but I cannot be sure.

[Waqar Ahmed]

the answer is same for the the below question

syms A1(z) A2(z) 
n1=1;
n2=1;
L=100;
deltak=2*pi/L;
ode1 = diff(A1) == i*n1*A1*A2*exp(-i*deltak*z);
ode2 = diff(A2) == i*n2*A1^2*exp(i*deltak*z);
cond1=A1(0)==1;
cond2=A2(1)==0;
dsolve([ode1,ode2],[cond1,cond2])

Answer 1

[Waqar Ahmed]

This question is solved numerically and the result is gotten as expected using ode45 function

Answer 2

[Walter Roberson]

Ignoring the questionable boundary conditions for the moment:

That pair of equations has one closed form solution:

A1(z) = 0
A2(z) = constant that depends on boundary condition

There is also a more general solution that cannot be expressed explicitly -- not really a solution as such, but rather a set of conditions that A1 and A2 would have to satisfy in order for them to be solutions.

[Waqar Ahmed]

if the conditon are not been used it does not have even the solution

[Walter Roberson]

Note that your boundary condition of A1(0)=1 rather than A1(0) = 0, rules out the degenerate form.

if the conditon are not been used it does not have even the solution

It has no closed form solution, just a description of what a solution would have to look like. The description looks like

MATLAB is not programmed to be able to find these general descriptions of solutions.

TL;DR: You cannot solve those symbolically.