Revision: Algebraic Expressions and Operations on Them Maths SSC (English Medium) 7th Standard Maharashtra State Board

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 

A differential equation \[ \frac{dy}{dx} = F(x,y) \] is said to be in variable separable form if \[ F(x,y) = g(x)h(y). \]

Thus, \[ \frac{dy}{dx} = g(x)h(y) \] and, if \[ h(y) \neq 0, \]

\[ \boxed{\,\frac{1}{h(y)}\,dy = g(x)\,dx\,}. \]

• A variable separable equation can be rearranged so that all y-terms are with dy and all x-terms are with dx.

• Separate variables first, then integrate.

• Use one constant of integration.

• Apply the initial condition only after getting the general solution.

• Final answers may be explicit or implicit.