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Is differential equations the hardest math?

Is differential equations the hardest math?

Differential equations is the hardest math class for a typical engineering curriculum: (Calc I-III + DE’s).

How do you simplify differential equations?

Steps

  1. Substitute y = uv, and.
  2. Factor the parts involving v.
  3. Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step)
  4. Solve using separation of variables to find u.
  5. Substitute u back into the equation we got at step 2.
  6. Solve that to find v.

Why are PDES harder than ODEs?

Because they have more degrees of freedom than ODEs they are generally a lot harder to crack. An arbitrary ODE is generally not analytically solvable either but I get your point. You seem to be focusing on the wrong part here. A PDE is like an ODE but with more variables (fewer things are constant, not more).

Is Calc 3 or differential equations harder?

It’s not a matter of one being more difficult than the other- Topics from Calculus III are used in Differential equations (partial derivatives, exact differentials, etc.). Calculus III can be taken at the same time, but that is harder. Calculus III should be a prerequisite for Differential Equations.

What does linear differential equation Mean?

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form.

What is a first order linear equation?

First-Order Linear Differential Equations: A First order linear differential equation is an equation of the form y + P(x)y = Q(x). The equation is called first order because it only involves the function y and first derivatives of y. A.

What are examples of nonlinear equations?

Examples of nonlinear differential equations are the Navier–Stokes equations in fluid dynamics and the Lotka –Volterra equations in biology. One of the greatest difficulties of nonlinear problems is that it is not generally possible to combine known solutions into new solutions.

What is a linear homogeneous differential equation?

A homogeneous linear differential equation is a differential equation in which every term is of the form y(n)p(x) i.e. a derivative of y times a function of x. In general, these are very difficult to work with, but in the case where all the constants are coefficients, they can be solved exactly.

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