# Help with NDSolve for system of odes [closed]

Can someone please tell me what I am doing wrong? I am trying to solve a system of odes using NDSolve. The code I have written is as follows:

NDSolve[{x'[t] == cos[t] + 4sin[t] - 4[x] - 2[y], y'[t] == -3sin[t] +
3[x] + [y], x == 0, y == -1},{x[t],y[t]},t]


However I am getting an error that says

Syntax:"-3sin[t]+3[x]+" cannot be followed by "[y]".


I have tried taking the brackets off [y] which results in

NDSolve: The function y appears with no arguments.


Any help would be greatly appreciated. Also how would I plot a solution curve for this ODE after getting NDSolve to function?

## closed as off-topic by bbgodfrey, m_goldberg, Bob Hanlon, Michael E2, MarcoBMay 8 '17 at 1:59

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – bbgodfrey, m_goldberg, Bob Hanlon, Michael E2, MarcoB
If this question can be reworded to fit the rules in the help center, please edit the question.

• what do you mean with 4[x] and 2[y]? Are those functions?? Also, the sinus function ist written in Mathematica with capital S, Sin[x] is $\sin(x)$. You should first take a look at basic syntax in Mathematica. – Mauricio Fernández May 7 '17 at 15:31
• You made the Sin sin before! Please show some signs of learning instead of asking people to do your work for you. – Michael E2 May 7 '17 at 18:05

## 1 Answer

eqns = {
x'[t] == Cos[t] + 4 Sin[t] - 4 x[t] - 2 y[t],
y'[t] == -3 Sin[t] + 3 x[t] + y[t],
x == 0, y == -1};


This system can be solved exactly with DSolve without using numeric techniques of NDSolve

soln = DSolve[eqns, {x, y}, t][]

(*  {x -> Function[{t}, E^(-2 t) (-2 + 2 E^t + E^(2 t) Sin[t])],
y -> Function[{t}, -E^(-2 t) (-2 + 3 E^t)]}  *)


Verifying that the solution satisfies the equations and initial conditions,

And @@ (eqns /. soln // Simplify)

(*  True  *)

Plot[Evaluate[{x[t], y[t]} /. soln], {t, 0, 3 Pi},
PlotLegends -> Placed[{x[t], y[t]}, {0.85, 0.2}]] 