Definitions [3]
The terms that do not have the same literal coefficients are called unlike terms.
For example:
6a, 6ab and 6ac are unlike terms.
Terms having the same literal part (same variables with the same powers) are called like terms.
For example:
xy, 5xy, -4xy, etc. are like terms
The equation \[\frac{dy}{dx} = F(x, y)\] is said to be in variable separable form if it can be expressed as \[g(x) dx = h(y) dy\] or equivalently as \[\frac{dy}{dx} = g(x)h(y)\] so that the variables can be separated and integrated.
Key Points
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Variable separable equations can be rewritten as x-part = y-part.
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Separate variables first, then integrate.
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Use one constant of integration.
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Apply the initial condition only after getting the general solution.
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Final answers may be explicit or implicit.
Concepts [10]
- Terms, Factors and Coefficients of Expression
- Classification of Terms in Algebra
- Algebraic Expressions
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Binomial by a Binomial
- Methods of Solving Differential Equations> Variable Separable Differential Equations
