Differential Equations — Order, Degree & Separation explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
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Notes
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Formulae
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Examples
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Practice
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A differential equation is an equation involving derivatives.
It describes how a quantity changes, not just what its value is.
Differential equations are used in motion, growth, decay, electricity, economics, and many science models.
The order of a differential equation is the highest order derivative present.
The degree is the power of the highest order derivative after the equation is written as a polynomial in derivatives.
Degree is defined only when derivatives are free from roots and fractions involving derivatives.
A separable differential equation can be arranged with y terms on one side and x terms on the other.
After separation, integrate both sides.
Meaning: An equation that contains a derivative.
Definition: An equation involving , , or other derivatives is a differential equation.
= 3x is a simple example.
Meaning: The highest derivative order in the equation.
Definition: If the highest derivative is , the order is 2.
Look for the highest derivative first.
Meaning: The power of the highest order derivative, when defined.
Definition: Degree is found after the equation is polynomial in derivatives.
If appears as highest derivative, degree is 3.
Meaning: Put y terms with dy and x terms with dx.
Definition: A separable equation can be written as f(y)ddx.
Then integrate both sides.
Easy
Question: Find the order of + = x.
Medium
Question: Find the degree of .
Exam-level
Question: Solve = 2x.
Confusing order and degree
Why it happens: Both are read from derivatives.
Correct approach: Order is derivative level. Degree is power of highest derivative.
Finding degree before clearing roots or fractions
Why it happens: The equation form is not checked.
Correct approach: Degree is defined only in polynomial form in derivatives.
Forgetting the constant after integration
Why it happens: Both sides are integrated quickly.
Correct approach: Add a constant of integration.
What does a differential equation describe?
It describes how one quantity changes with another.
Is degree always defined?
No. It is defined only when the equation is polynomial in derivatives.
What is separation of variables?
It is arranging y terms with dy and x terms with dx before integrating.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.