Mathematics
High School (11–12)
Functions and Calculus › Differential EquationsChapter 13Contains Standard contentDifferential Equations
A cup of tea cools quickly at first and then more slowly. The speed of cooling depends on how hot the tea is right now. A rule that links a quantity to its own rate of change is a differential equation. In this chapter you name and form such equations, solve the first-order ones by separating the variables, by a substitution or by an integrating factor, and use them to model growth, decay, cooling and mixing. It covers the unit of the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP. Python draws direction fields and follows solutions step by step.
Part of Mathematics · High School (11–12) (chapter 13)
Following adds this path to your dashboard and enrolls you in the 3 courses you can open, so you can start right away. Parts on a paid plan open when your plan includes them.
1 more part of this path isn't open to you yet: some need a Standard or Premium plan.
Courses in This Path (4)
1.Not started2.
Differential Equations: Order, Degree and Solutions
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.
First-Order Equations: Separable, Homogeneous and Linear
Most equations of this unit have a first derivative and nothing higher. Three methods solve nearly all of them. Separate the variables when the two sides can be pulled apart, put