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I am solving two PDEs together for two functions y, G:

Derivative[0,1][y][x,t] + 2 Derivative[1,0][G][x,t] == 0
Derivative[0,1][y][x,t] + Derivative[1,0][G][x,t] == 2

I want to solve those PDEs to find the value of both y[x,t] and G[x,t]

I tried to use DSolve but it doesn't work with me, even it is easy to do it by my hand. I would like to get the answer through Mathematica.

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    $\begingroup$ Hi, do you have initial conditions for the system? $\endgroup$ Feb 5 '20 at 11:06
  • $\begingroup$ Please post code in proper input form that can be pasted into Mathematica. You may find this meta Q&A helpful $\endgroup$
    – Michael E2
    Feb 5 '20 at 12:05
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The equations are so trivial they're beneath DSolve's dignity. They don't even look differential enough.

eqns = {D[y[x, t], t] + 2 D[G[x, t], x] == 0, D[y[x, t], t] + D[G[x, t], x] == 2};
halfsol = Reduce[eqns, {D[y[x, t], t], D[G[x, t], x]}]
sol = DSolve[halfsol, {y[x, t], G[x, t]}, {x, t}]
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  • $\begingroup$ Dear aooiii, i just wanted to tell Thank you......... $\endgroup$
    – Ahmed Gol
    Feb 5 '20 at 11:42
  • $\begingroup$ You're welcome ^_^ $\endgroup$
    – aooiiii
    Feb 5 '20 at 11:44
  • $\begingroup$ Dear aooiii, i tried the same way to solve those group but Mathematica couldnt give ans kindly give your comments, eqns = {D[y[x, t], t] - [Epsilon] (G[x, t] - y[x, t]) == 0, D[G[x, t], t] - 1/A D[G[x, t], x, x] - B (y[x, t] - G[x, t]) == 0}; halfsol = Reduce[eqns, {D[y[x, t], t], D[G[x, t], x]}]; sol = DSolve[halfsol, {y[x, t], G[x, t]}, {x, t}] $\endgroup$
    – Ahmed Gol
    Feb 6 '20 at 5:24
  • $\begingroup$ Sorry, but my hack only worked with that particular system. Please don't take the method too seriously; it's NOT how things should be done. And I don't know how to make Mathematica solve the new one (except there must be no brackets [] around Epsilon, but that doesn't help much), so let's just consider it unsolvable by Mathematica. $\endgroup$
    – aooiiii
    Feb 6 '20 at 9:21

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