What is Differential: Definition and 1000 Discussions

In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.
Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.

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  1. J

    Matrix riccati differential equation using matlab

    Homework Statement Homework EquationsThe Attempt at a Solution
  2. F

    Ambiguity in the method applied for differential equations

    Homework Statement Why do we need two solutions to solve a 2nd order linear differential equation? lets consider a differential equation with equal roots for auxiliary equation. So the reasoning behind why can't we use y=Aen1x+Ben2x as its general solution is because since the roots are equal...
  3. I

    B Can you reason out a differential equation using logic?

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  4. P

    B Exploring the Meaning of "d" in Differential Physical Quantities

    [Mentor's note: This question was split off from: https://www.physicsforums.com/threads/meaning-of-physical-quantities-and-division.880214/] What does this differential "d" mean? Why say dE instead of E? or
  5. Jianphys17

    Differential Geometry book with tensor calculus

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  6. petterson

    A Differential equation with integral

    Hi, I was wondering if anyone had some advice on how to solve the following equation for ## F(b)##: $$ F(g(b)) h(b) + F'(b) s(b) - F(b)h(b) + h(b) + \int_{g(b)}^{b} v(x) F'(x) dx = 0 $$ Any hints on how to tackle this would be highly appreciated. Thank you!
  7. awholenumber

    Calculus First order differential equations ?

    what is a good book to learn first order differential equations ??
  8. awholenumber

    I First order differential equations ?

    what is a good book to learn first order differential equations ??
  9. B

    Courses Should I take a course in differential geometry?

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  10. awholenumber

    I Differential equations and numerical methods questions

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  11. P

    Modeling survival with a differential equation

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  12. Rdgmol

    A Partial Differential - Thermodynamics

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  13. J

    Relativity Differential Forms and the Geometry of General Relativity

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  14. F

    I Diagonalising a system of differential equations

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  15. chwala

    Solving a differential equation using integrating factor

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  16. awholenumber

    B A few differential equation questions

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  17. funlord

    B Where is the best place to put the arbitrary constant?

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  18. A

    I Calculating the Surface Area of a Sphere: How Does it Differ?

    please , I'm french , so i didn't quite get the meaning of this sentence.
  19. AwesomeTrains

    Green's function differential equation

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  20. O

    Discrete Differential Amplifier

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  21. dumbdumNotSmart

    B System of differential equations Basic question

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  22. P

    Integrating a Tricky Differential Equation with a Square Root Fraction

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  23. R

    Pressure differential through orifice plate

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  24. B

    I Laplace transform using differential equations

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  25. Jianphys17

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  26. funlord

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  27. teroenza

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  28. goonking

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  29. E

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  30. awholenumber

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  31. Aashish sarode

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  32. Reno Nza

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  33. N

    How Does Total Differential Determine Accuracy in Parameter Settings?

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  34. N

    Total Diff: Calculate d(x*y^4)

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  35. chwala

    Differential Equation: Solving for x in terms of θ | (3+cos2θ)dx/dθ = xsin2θ

    Homework Statement Solve and obtain an expression for x in terms of θ given ## (3+ cos 2θ) dx/dθ = x sin 2θ## Homework EquationsThe Attempt at a Solution ...##dx/x = ((sin 2θ)/(3+ cos 2θ))dθ## , let ##u = (3+cos 2θ)⇒ du/dθ= -2 sin 2θ## thus ##∫dx/x = -1/2∫du/u ##...[/B]are my steps...
  36. E

    I What happens if you divide by a differential?

    I've always wondered what happens when you divide a first order seperable DE by a differential? Does it then become a PDE? Is it still possible to solve it? If so how would one solve such a DE? For example this: Starting with this equation for pressure: ##P=ρgh## ; ## h = -y## ##P= -ρgy##...
  37. P

    First order Partial differential equation

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  38. chwala

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  39. R

    Video lectures for differential equations 2

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  40. K

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  41. F

    I How to interpret the differential of a function

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  42. Avi Nandi

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  43. B

    Which metals undergo differential aeration corrosion?

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  44. S

    A Normalized Differential Scattering Probability

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  45. T

    How to prepare for differential equations?

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  46. Jose Z

    Help Solving the following Differential equation

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  47. P

    Automotive Open Car Differential Burnout Debate

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  48. C

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  49. faradayscat

    Differential equation with power series

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  50. Aceix

    Solving a homogeneous first-order ordinary differential eqn

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