Page 159 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes  Solution of (3) is
1 1
. z   2. dx  . c
x 2 x 2

z 2
or 2   c
x x
2
or (2 + cx) xy = 1,
which is the required solution.

Did u know? The replacements were victorious in converting the Bernoulli equation into a
linear equation.

Task Solve the following differential equation:

dy tan y x
y
  1 x e  sec .
dx 1 x

Self Assessment

Fill in the blanks:
dy n
9. An equation of the form  Py  Qy , where P and Q are functions of x only or constants
dx
known as .................................. .
10. If n > 1 in the Bernoulli’s equation, then we have to ................................. the solution y=0 to
the solutions.
11. If n = 0, Bernoulli’s equation ................................. instantaneously to the standard form first-
dy
order linear equation:  Py  Q .
dx
12. General equation reducible to linear form is ................................. .
13. In the general equation, P and Q are functions of x only or ................................. .

dy
y
14. Putting f (y) = z in the general equation f ' ( )  Pf   y  Q , implies
dx
................................. .
11.3 Summary

 The easiest type of relationship that two variables can comprise is a linear relationship.

dy
 An equation of the form  Py  Q in which P & Q are functions of x alone or constant
dx
is called a linear equation of the first order.

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