Using Mathematica for ODEs, Part 1 (Use DSolve and Plot for a pure antiderivative problem)

Bill Kinney, Bethel University Math Department.

(0:00) Introduction to using Mathematica for ordinary differential equations
(1:03) Show the example
(2:30) Use DSolve to find the general solution of dy/dt = t^2
(4:14) Solve it with an indefinite integral
(5:13) Use DSolve to find the unique solution of the IVP dy/dt = t^2, y(0) = -3
(7:09) Confirm the solution with a prime operator once the function has been defined
(8:14) Use Plot to graph the solution and its derivative. Use PlotStyle to color the graphs.

(a) Find the general solution of the ordinary differential equation (ODE) dy/dt = t^2. Note: this is a "pure antiderivative" problem. (b) Find the unique solution of the initial-value problem (IVP) dy/dt = t^2, y(0) = -3. (c) Graph the solution from part (b), as well as its derivative.

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[LaLakrs]

Great video. I'm new to Mathematica and am taking a nonlinear dynamics, chaos and fractals course and these beginner tutorials are extremely helpful. Thanks so much. 

[TheTomorrowDream]

Great video!!! this help because I'm new using mathematica, thanks!!!!

[JohnM...]

I prefer in odes an implicit solution, which mathematica doesn't seem to give (or I'm unaware of it)

[jamesbaldwin]

How would you do this if your function was, say, y' = t^2 +y ?

[kaleemullahuom]

how can i recover calculations from graph plotted in mathematica.
i have lost the calculations. while the grahs are present in coral draw.
plz plz

[inteusproductions]

I got this error when I inputted the same for the initial value problem.

DSolve::deqn: Equation or list of equations expected instead of False in the first argument {(y^\[Prime])[t]==t^2, False}. >>

[samkz]

Is there command to transform ODE to separable form?