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I am using the DSolve to solve the following 2 ODEs \begin{equation} \begin{cases} &\dot{y}(t)=z(t)-y(t)-\frac{c_1c_2y(t)}{-c_1c_2e^{-t}t+c_1(1-c_2)+c_3e^{-t}}\\ &\dot{z}(t)=-z(t)+\frac{c_1c_2y(t)}{-c_1c_2e^{-t}t+c_1(1-c_2)+c_3e^{-t}} \end{cases} \end{equation} with initial value $z(0)=0$ and $y(0)\in(0,1)$.

Then I use the following code

system = {y'[t] == -y[t] + z[t] - 
     c1*c2*y[t]/(c1*(1 - c2) - c1*c2*Exp[-t]*t + c3*Exp[-t]), 
   z'[t] == -z[t] + 
     c1*c2*y[t]/(c1*(1 - c2) - c1*c2*Exp[-t]*t + c3*Exp[-t]), 
   z[0] == 0};

and

DSolve[system, {y[t], z[t]}, t]

However, Mathematica did nothing but beautify my input. So does this mean, Mathematica cannot solve this ODE in closed-form?

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  • $\begingroup$ You can format inline code and code blocks by selecting the code and clicking the {} button above the edit window. The edit window help button ? is also useful for learning how to format your questions and answers. You may also find this this meta Q&A helpful $\endgroup$ – Michael E2 Apr 12 '16 at 22:21
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    $\begingroup$ Yeah, it probably means DSolve doesn't know how to solve it. $\endgroup$ – Michael E2 Apr 12 '16 at 22:32
  • $\begingroup$ @MichaelE2 then is there any more powerful tool to solve ODE symbolically? $\endgroup$ – KevinKim Apr 13 '16 at 1:01
  • $\begingroup$ No, I don't think there is. Sometimes one can apply a change of variables that converts the system to a form DSolve can recognize, but it's rare. I have nothing to suggest in that regard. Perhaps someone will be able to suggest something. $\endgroup$ – Michael E2 Apr 13 '16 at 3:10

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