# Visualizing the solutions of the Differential equations by varying different parameters

Actually I am interested in analyzing the soution to the ODE given as $\frac{dy}{dx} = A + By + C\sin(y) , y(l) = m$ and check how the solution gets affected like whether they exist or not depending on the initial conditions .If they exist how the solutions look like and how they vary when we vary the parameters $A,B,C$.

I tried to visualize it through DESMOS as here - https://www.desmos.com/calculator/ernu8p9mnw But could not give the entry properly?

Is there any online source which can help me in visualizing this ? Also can this be done in MATLAB? like varying the parameters?

Any help is great.

• Traditionally Mathematica has been very good for things like this, should you have access to it. – Spencer Bryngelson Jun 1 '17 at 13:36
• Sorry I don't have access,I am self studying actually. – BAYMAX Jun 1 '17 at 14:03

You can try Geogebra (it is free). With SolveODE command and sliders you can do what yo want. For the usage of SolveODE command see. For example by using following command

SolveODE[ <f'(x, y)>, <Start x>, <Start y>, <End x>, <Step> ] with

SolveODE[A + B y + C sin(y), l, m, 10, 0.1]

I got the solution curve below. You can vary the values of parameters A,B,C,l,m with sliders. • What do I do if I have a system of ODE's and have separate parameters for each system? – BAYMAX Jun 3 '17 at 6:22
• There is NSolveODE command. Have you look at manual page wiki.geogebra.org/en/NSolveODE_Command – Ömer Jun 3 '17 at 9:36

You can use DifferentialEquations.jl Online to visualize solutions to differential equations without a hassle. It's built using the Julia suite DifferentialEquations.jl, and the online interface is a subset of features which includes explicit parameters and visualization.

Here's an example of your equation, assuming that l was the initial time point and this was not a BVP. If it is a BVP, currently the BVP solvers do not have an online interface.

Note: I am the developer

• added a quick note. – Chris Rackauckas Jun 1 '17 at 17:55

Using recent Wolfram Cloud functionality and the code below you can do it online in your browser. I've deployed the app in the cloud:

https://www.wolframcloud.com/objects/e087e0f0-fe3e-4b82-a7c2-7d668ec205d3

P.S. You need to have Wolfram ID to log in before you can use it.

Manipulate[
Plot[
Evaluate[NDSolveValue[{
u'[t]==a+b u[t]+c Sin[u[t]]
,u[l]==m},u,{t,0,10}][t]
]
,{t,0,10}
,PlotRange->All]
,{a,-10,10}
,{b,-10,10}
,{c,-10,10}
,{l,0,10}
,{m,-10,10}
] 