I want solve a differential equation for varying parameter and then I wish to create a list which contains the parameter and corresponding value of differential equation. So that I can make a List Density plot.

differential equation is

f = y'[x] == a*Cos[x] + b*Sin[x];

I want to have a list with parameter and its corresponding differential equation solution, like {{a,b,value},{a',b',value},{}}. So I can use ListDensity Plot . Any suggestions are welcome

  • $\begingroup$ Welcome to the Mathematica Stack Exchange. Please include Mathematica code for what you have tried so far. $\endgroup$
    – Syed
    Commented Nov 17, 2022 at 8:37
  • $\begingroup$ I have added a simple example which I am trying solve $\endgroup$ Commented Nov 17, 2022 at 8:48
  • $\begingroup$ What is the meaning of " So I can use ListDensity Plot"? $\endgroup$ Commented Nov 17, 2022 at 8:55
  • $\begingroup$ At the end I want to create a list. Basically I need to make a density plot of the diff equation for varying parameters $\endgroup$ Commented Nov 17, 2022 at 8:56
  • $\begingroup$ DensityPlot of a,b and ??? or y[a,b][x]? $\endgroup$ Commented Nov 17, 2022 at 8:58

2 Answers 2


Useing ParametricNDSolveValue.

sol = ParametricNDSolveValue[{y'[x] == a*Cos[x] + b*Sin[x], 
    y[0] == 1}, y, {x, 1, 10}, {a, b}];
Block[{x = 5}, DensityPlot[sol[a, b]@x, {a, 1, 5}, {b, 1, 5}]]

enter image description here

DensityPlot3D[sol[a, b]@x, {a, 1, 5}, {b, 1, 5},{x, 1, 10}]

enter image description here

  • $\begingroup$ Thank you for your solution. It worked. What happens if there are more than one differential equations? Then how do you plot a specific differential equation? $\endgroup$ Commented Nov 17, 2022 at 9:59
  • $\begingroup$ @physicsgeek You can ask a new equations and post a new code about it. Thanks your accption. $\endgroup$
    – cvgmt
    Commented Nov 17, 2022 at 10:01
  • $\begingroup$ I have posted a different question. I t would be nice to have some help @cvgmt $\endgroup$ Commented Nov 17, 2022 at 10:12
  • $\begingroup$ mathematica.stackexchange.com/questions/276143/… $\endgroup$ Commented Nov 17, 2022 at 10:13

Try NDSolveValue :

  • $\begingroup$ I tried but it gives me a list which I cannot use to create a density plot using the command list density plot $\endgroup$ Commented Nov 17, 2022 at 8:58

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