Maharashtra State BoardHSC Arts 12th Board Exam

Methods of Solving First Order, First Degree Differential Equations - Differential Equations with Variables Separable Method


A first order-first degree differential equation is of the form 
`(dy)/(dx)` =F(x,y)    ...(1)
If F(x, y) can be expressed as a product g (x) h(y), where, g(x) is a function of x and h(y) is a function of y, then the differential equation (1) is said to be of variable separable type. The differential equation (1) then has the form 
`(dy)/(dx)` = h(y) . g(x)  ..(2)
If h(y) ≠ 0, separating the variables, (2) can be rewritten as
`1/(h(y)` dy = g(x) dx    ..(3)
Integrating both sides of (3), we get

`int 1/(h(y)`dy = `int` g(x) dx   ...(4)

Thus, (4) provides the solutions of given differential equation in the form   H(y) = G(x) + C
Here, H (y) and G (x) are the anti derivatives of `1/(h(y)` and g(x) respectively and C is the arbitrary constant.

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