(ODE45) problem of solving laser rate equation

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I want to simulate the reference’s passive Q switch process. The reference is
Shengzhi Zhao, Lei Chen, Hongming Zhao, Guiqiu Li, Lu Zhang, Kejian Yang. Laser–diode-pumped passively Q-switched Nd3+:NaY(WO4)2 laser with GaAs saturable absorber. Optics & Laser Technology 37 (2005) 187–191.
I used ODE45 to solve this problem, but the result was not agreed with the reference.I have described the problem in a .doc file in detail. Could anyone help me to solve this problem?

The reference, MATLAB script file and function were also included in the attached files.
 

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Somebody can not open this .doc file, so I changed this file again. The file is attached.
 

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Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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