# Solve set of non linear differential equations [closed]

I have set of differential equations. For example, I took two equations and tried to solve them as below. I am not getting any results. Please help me to figure it out the mistake. And I wonder if I can use matrices to solve such a system of equations.Please don't put down this question.This is very important to my research.

Clear[j, v, s]
j[V_] = v[t] + v[t]^2;
τ = 1;
s = 0.1;
ip = 0;
DSolve[{v1'[t] == -v1[t]/τ + (j[v2]*s) + ip,
v2'[t] == -v2[t]/τ + (j[v1]*s) + ip},    {v1, v2}, t]

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## closed as off-topic by m_goldberg, bobthechemist, RunnyKine, Michael E2, rm -rf♦Feb 13 at 16:19

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@Artes You are right. I am not an expert in Mathematica. But, I think that I have used variables and functions correctly here. I appreciate if you can show my mistakes here. Thanks –  TMH Feb 10 at 0:22
In general, symbolic functions don't like inexact values. An inexact value is a number with a decimal point in it, like S = 0.1 above. It is not clear to me why it throws that RowReduce error, but it will go away if you change 0.1 to 1/10 (which is generally a good idea when working symbolically). It still won't be able to arrive to a solution for this particular system of equations, it'll time out after a while. Another suggestion is not to use symbols starting with capital letters to avoid name collisions with system symbols (it'll save you trouble if you follow this). –  Szabolcs Feb 10 at 0:26
@TMH I know, I did wait for it and finally it decides that it cannot solve the system symbolically. If you are looking for a numerical solution use NDSolve. –  Szabolcs Feb 10 at 0:46
@TMH I think that at this point this isn't really a question about Mathematica (how to program something), but about maths (how to solve your differential equations). Mathematica will not be able to solve any differential equation you try, only some of them. –  Szabolcs Feb 10 at 1:02
This question appears to be off-topic because it is too localized; i.e, it applies only to the local situation and needs of its poster and answers will not benefit others. –  m_goldberg Feb 10 at 1:47

You indicated in the comments below your question that your goal is to plot v1 and v2 against t. The following code does that using NDSolve. I corrected the capital-V error in your definition of j and added some initial conditions.

Clear[j, v, s]
j[v_] = v[t] + v[t]^2;
τ = 1;
s = 0.1;
ip = 0;
sol = NDSolve[{v1'[t] == -v1[t]/τ + (j[v2]*s) + ip,
v2'[t] == -v2[t]/τ + (j[v1]*s) + ip,
v1[0] == 1,
v2[0] == 0.5}, {v1, v2}, {t, 0, 10}][[1]]

Plot[{v1[t], v2[t]} /. sol, {t, 0, 10}]


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Thanks for the answer. This is very helpful. –  TMH Feb 10 at 15:13