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Hey guys I'm using mathematica 5 now, and so new to this software thing. May I know how to plot the direction field using PlotVectorField[] and also finding complete solution curve for this equation?

$$\frac{dy}{dx}-\frac{y}{x}=\frac{4x^2}{y}\cos(x)$$

Please do help or give me any tips if possible. Thanks in advance.

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  • $\begingroup$ Look up DSolve[] and ListVectorPlot[]. In addition, for this ODE, you should give a boundary condtion. $\endgroup$ – xyz Mar 18 '16 at 2:59
  • $\begingroup$ Welcome to Mathematica.SE! I suggest the following: 0) Browse the common pitfalls question 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Read the faq! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! $\endgroup$ – Dr. belisarius Mar 18 '16 at 3:46
  • $\begingroup$ Mathematica Version 5 is very old. If possible try to grab a newer one. There has been a lot of improvements since then! $\endgroup$ – Dr. belisarius Mar 18 '16 at 3:47
  • $\begingroup$ DSolve[{y'[x] == y[x]/x + 4 x^2 Cos[x]/y[x], y[a] == b}, y[x], x] // FullSimplify $\endgroup$ – Dr. belisarius Mar 18 '16 at 3:57
  • $\begingroup$ erm can you explain why i need to add y[a] == b ? cause my lecture didnt say anything about it. thanks $\endgroup$ – Elven Lim Mar 18 '16 at 4:42
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yy[x_, a_, b_] := Evaluate[y[x] /. 
                  DSolve[{y'[x] == y[x]/x + 4 x^2 Cos[x]/y[x], y[a] == b}, y[x], x]]

Manipulate[Plot[yy[x, a, b], {x, -1, 3}, Evaluated -> True], {a, 1, 3}, {b, 1, 3}]

Mathematica graphics

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