Differential Equations: Order, Degree and Solutions

Name: Differential Equations: Order, Degree and Solutions
Author: StemPy Lab

A population grows faster when it is larger. A spring pulls harder when it is stretched more. Each fact links a quantity to its own rate of change, and that link is a differential equation. Learn to name the order and the degree, to check that a function is a solution, to build an equation from a family of curves and to read a direction field. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.

3 lessons, about 1 h 15 min3 simulations10 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Order, degree and what a solution is
A differential equation links a function to its own derivatives. Its order is the order of the highest derivative in it. Its degree is the power of that highest derivative, when the equation is a polynomial in the derivatives. A solution is a function that makes the equation true. The general solution has as many arbitrary constants as the order, and a particular solution has them fixed by conditions.
1 simulation1 practice question1 Python program3 problems1 Python lab
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Lesson 2about 25 min
Forming a differential equation
A family of curves has arbitrary constants, such as all lines $y = mx$ through the origin. An equation that every member satisfies, and that does not mention the constants, is the differential equation of the family. To form it, differentiate as many times as there are constants and eliminate the constants. The order of the equation equals the number of constants.
1 simulation1 practice question1 Python program4 problems
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Lesson 3about 25 min
Direction fields and solution curves
A first-order equation $\dfrac{dy}{dx} = f(x, y)$ tells you the slope at every point of the plane. Draw a short segment of that slope at many points and you have a direction field. A solution curve follows the segments. You can read the shape of the solutions from the field before you solve anything, and you can walk along it step by step.
1 simulation1 practice question1 Python program3 problems1 Python lab1 question set1 note
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Order, Degree and Solutions: Practice Paper

15 questions · 20 min

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Differential Equations: Order, Degree and Solutions

Course outline (3 lessons)

Order, degree and what a solution is

Forming a differential equation

Direction fields and solution curves

Test Your Learning

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